Traditional Multiple Linear Regression Model Research Articles

Fingertip capillary dynamic near infrared spectrum (DNIRS) measurement combined with multivariate linear modification algorithm for noninvasive blood glucose monitoring

Blood glucose continuous monitoring (GCM) plays a crucial role in prevention and diagnosis of diabetes. A noninvasive CGM method based on fingertip capillary Dynamic Near Infrared Spectrum (DNIRS) combined with multivariate linear modification algorithm was proposed in this study. In order to control the environmental variables and physicochemical parameters during spectral data acquisition, a Fingertip Fixed Probe Biosensor (FFPB) was designed. In the preliminary experiment, three group of volunteers (healthy young people, middle-aged people and patients with diabetes) were test twice. The model established by the former test could be used for the latter prediction for each individual, and the duration of each test was 120 min. Meanwhile the reference value of blood glucose was measured by the standard blood glucose analyzer. When establishing the prediction model, a multivariate linear modification algorithm was proposed, which has better prediction accuracy and precision than the traditional multiple linear regression model. The root mean square error of validation and root mean square error of prediction are RMSEV≤15.61 mg/dL and RMSEP≤20.67 mg/dL respectively. The correlation coefficient between the prediction and the reference value of blood glucose also reaches 0.87, and the prediction keeps good track of postprandial glucose excursions with the comparison of the reference value. Through the Clark Error Grid Analysis (CEGA), more than 96 % of the test set samples lies within Zone A. The result indicates that the prediction model has good prediction accuracy and robustness. This measurement method can continuously and noninvasively monitor the variance of blood glucose in human body, which has a promising prospect in the future practical application.

Coupling wavelet transform and artificial neural network for forecasting estuarine salinity

Accurate and reliable predictions of estuarine salinity can lead to more effective water resource management and can alleviate the adverse impacts of saltwater intrusion. Due to the nonlinear and nonstationary features in time series of estuarine salinity, this study is conducted to develop a hybrid model coupling the techniques of wavelet transform (WT) and artificial neural network (ANN) for forecasting estuarine salinity in the Pearl River Estuary, China. Two wavelet-based forecasting frameworks, the direct forecast (DF) framework (i.e., only explanatory variables are decomposed, leading to direct forecasting of the target variables) and multicomponent forecast (MF) framework (i.e., both explanatory and target variables are decomposed, and each target component is forecasted separately), were used to construct the WT-ANN models. The results reveal the superiority of hybrid WT-ANN models in estuarine salinity forecasting over traditional multiple linear regression (MLR) models and single ANN models, indicated by the Nash–Sutcliffe efficiency (NSE), correlation coefficient (R), root mean square error (RMSE), mean absolute error (MAE) and Kling–Gupta efficiency (KGE). Between the two wavelet-based forecasting paradigms, the MF framework outperformed the DF framework for better capturing the mutual dependence (i.e., mutual information, MI) between input and output variables. Additionally, the superiority of WT-ANN models in comparison with MLR and ANN models is increasingly prominent when the forecast lead time is extended from 1 to 3 days.

Estimation of Forest Biomass in Beijing (China) Using Multisource Remote Sensing and Forest Inventory Data

Forest biomass reflects the material cycle of forest ecosystems and is an important index to measure changes in forest structure and function. The accurate estimation of forest biomass is the research basis for measuring carbon storage in forest systems, and it is important to better understand the carbon cycle and improve the efficiency of forest policy and management activities. In this study, to achieve an accurate estimation of meso-scale (regional) forest biomass, we used Ninth Beijing Forest Inventory data (FID), Landsat 8 OLI Image data and ALOS-2 PALSAR-2 data to establish different forest types (coniferous forest, mixed forest, and broadleaf forest) of biomass models in Beijing. We assessed the potential of forest inventory, optical (Landsat 8 OLI) and radar (ALOS-2 PALSAR-2) data in estimating and mapping forest biomass. From these data, a wide range of parameters related to forest structure were obtained. Random forest (RF) models were established using these parameters and compared with traditional multiple linear regression (MLR) models. Forest biomass in Beijing was then estimated. The results showed the following: (1) forest inventory data combined with multisource remote sensing data can better fit forest biomass than forest inventory data alone. Among the three forest types, mixed forest has the best fitting model. Forest inventory variables and multisource remote sensing variables can match each other in time and space, capturing almost all spatial variability. (2) The 2016 forest biomass density in Beijing was estimated to be 52.26 Mg ha−1 and ranged from 19.1381–195.66 Mg ha−1. The areas with high biomass were mainly distributed in the north and southwest of Beijing, while the areas with low biomass were mainly distributed in the southeast and central areas of Beijing. (3) The estimates from the RF model are better than those from the MLR model, showing a high R 2 and a low root mean square error (RMSE). The R 2 values of the MLR models of three forest types were greater than 0.5, and RMSEs were less than 15.5 Mg ha−1, The R 2 values of the RF models were higher than 0.6, and the RMSEs were lower than 13.5 Mg ha−1. We conclude that the methods in this paper can help improve the accurate estimation of regional biomass and provide a basis for the planning of relevant forestry decision-making departments.

A Nonlinear Method for Component Separation of Dam Effect Quantities Using Kernel Partial Least Squares and Pseudosamples

Existing component separation methods fail to consider the complex nonlinear relationship between dam effect quantities and environmental variables. In this study, a novel nonlinear component separation method for the effect quantities is proposed by combining kernel partial least squares (KPLS) and pseudosamples. By this method, a nonlinear monitoring model is established based on KPLS, and the complicated nonlinear relationship between the effect quantities and environmental variables can be determined accurately through the model. Furthermore, special pseudosamples are constructed to separate independent components and coupling influence components of environmental factors from the KPLS model. These methods have been applied into a super‐high arch dam, and the separated displacement components conform to the general deformation law. The presented results indicate that it is more reliable than traditional multiple linear regression models.

Multiple regression and machine learning based methods for carcass traits and saleable meat cuts prediction using non-invasive in vivo measurements in commercial lambs

The aim of this study is to investigate the performance of multiple linear regression and machine learning methods to predict carcass traits and commercial meat cuts in lambs using non-invasive in vivo measurements. Bayesian networks were also investigated as an alternative method for feature selection. Phenotypes from 74 nondescript breed lambs were measured. A leave-one-out cross-validation strategy was performed and predictive ability statistics (R2, RMSE) were assessed. Moderate to high prediction accuracies were observed, with R2 values across models ranging, from 0.36 to 0.88 for carcass traits and 0.65 to 0.84 for meat cuts predictions. Results suggest that support vector machine algorithm is a potential alternative to the traditional multiple linear regression model. Further, the results of this study suggest that both stepwise and Bayesian network procedures could be useful as pre-selection tools of the input variables in non-parametric approaches and the best method for feature selection may be trait and model dependent.

Decoding Voluntary Movement of Single Hand Based on Analysis of Brain Connectivity by Using EEG Signals

Research about decoding neurophysiological signals mainly aims to elucidate the details of human motion control from the perspective of neural activity. We performed brain connectivity analysis with EEG to propose a brain functional network (BFN) and used a feature extraction algorithm for decoding the voluntary hand movement of a subject. By analyzing the characteristic parameters obtained from the BFN, we extracted the most important electrode nodes and frequencies for identifying the direction of movement of a hand. The results demonstrated that the most sensitive EEG components were for frequencies delta, theta, and gamma1 from electrodes F4, F8, C3, Cz, C4, CP4, T3, and T4. Finally, we proposed a model for decoding voluntary movement of the right hand by using a hierarchical linear model (HLM). Through a voluntary hand movement experiment in a spiral trajectory, the Poisson coefficient between the measurement trajectory and the decoding trajectory was used as a test standard to compare the HLM with the traditional multiple linear regression model. It was found that the decoding model based on the HLM obtained superior results. This paper contributes a feature extraction method based on brain connectivity analysis that can mine more comprehensive feature information related to a specific mental state of a subject. The decoding model based on the HLM possesses a strong structure for data manipulation that facilitates precise decoding.

Influencing factors and prediction of ambient Peroxyacetyl nitrate concentration in Beijing, China.

Peroxyacyl nitrates (PANs) are important secondary pollutants in ground-level atmosphere. Accurate prediction of atmospheric pollutant concentrations is crucial to guide effective precautions for before and during specific pollution events. In this study, four models based on the back-propagation (BP) artificial neural network (ANN) and multiple linear regression (MLR) methods were used to predict the hourly average PAN concentrations at Peking University, Beijing, in 2014. The model inputs were atmospheric pollutant data and meteorological parameters. Model 3 using a BP-ANN based on the original variables achieved the best prediction results among the four models, with a correlation coefficient (R) of 0.7089, mean bias error of -0.0043 ppb, mean absolute error of 0.4836 ppb, root mean squared error of 0.5320 ppb, and Willmott's index of agreement of 0.8214. Based on a comparison of the performance indices of the MLR and BP-ANN models, we concluded that the BP-ANN model was able to capture the highly non-linear relationships between PAN concentration and the conventional atmospheric pollutant and meteorological parameters, providing more accurate results than the traditional MLR models did, with a markedly higher goodness of R. The selected meteorological and atmospheric pollutant parameters described a sufficient amount of PAN variation, and thus provided satisfactory prediction results. More specifically, the BP-ANN model performed very well for capturing the variation pattern when PAN concentrations were low. The findings of this study address some of the existing knowledge gaps in this research field and provide a theoretical basis for future regional air pollution control.

Development of a Powerful Data-Analysis Tool Using Nonparametric Smoothing Models To Identify Drillsites in Tight Shale Reservoirs With High Economic Potential

Summary The oil-and-gas industry is entering an era of “big data” because of the huge number of wells drilled with the rapid development of unconventional oil-and-gas reservoirs during the past decade. The massive amount of data generated presents a great opportunity for the industry to use data-analysis tools to help make informed decisions. The main challenge is the lack of the application of effective and efficient data-analysis tools to analyze and extract useful information for the decision-making process from the enormous amount of data available. In developing tight shale reservoirs, it is critical to have an optimal drilling strategy, thereby minimizing the risk of drilling in areas that would result in low-yield wells. The objective of this study is to develop an effective data-analysis tool capable of dealing with big and complicated data sets to identify hot zones in tight shale reservoirs with the potential to yield highly productive wells. The proposed tool is developed on the basis of nonparametric smoothing models, which are superior to the traditional multiple-linear-regression (MLR) models in both the predictive power and the ability to deal with nonlinear, higher-order variable interactions. This data-analysis tool is capable of handling one response variable and multiple predictor variables. To validate our tool, we used two real data sets—one with 249 tight oil horizontal wells from the Middle Bakken and the other with 2,064 shale gas horizontal wells from the Marcellus Shale. Results from the two case studies revealed that our tool not only can achieve much better predictive power than the traditional MLR models on identifying hot zones in the tight shale reservoirs but also can provide guidance on developing the optimal drilling and completion strategies (e.g., well length and depth, amount of proppant and water injected). By comparing results from the two data sets, we found that our tool can achieve model performance with the big data set (2,064 Marcellus wells) with only four predictor variables that is similar to that with the small data set (249 Bakken wells) with six predictor variables. This implies that, for big data sets, even with a limited number of available predictor variables, our tool can still be very effective in identifying hot zones that would yield highly productive wells. The data sets that we have access to in this study contain very limited completion, geological, and petrophysical information. Results from this study clearly demonstrated that the data-analysis tool is certainly powerful and flexible enough to take advantage of any additional engineering and geology data to allow the operators to gain insights on the impact of these factors on well performance.

One-day-ahead daily power forecasting of photovoltaic systems based on partial functional linear regression models

The intra-day time-varying pattern of solar data is more informative than the aggregated mean daily data. However, most of the traditional forecasting models often construct the 1-day ahead daily power forecast based on its historical daily averages but ignore the information from its intra-day dynamic pattern. Intuitively, the use of aggregated data could cause certain loss of information in forecasting, which in turn adversely affects forecasting accuracy. In order to make use of the valuable trajectory information of the power output within a day, this paper suggests a partial functional linear regression model (PFLRM) for forecasting the daily power output of PV systems. The PFLRM is a generalization of the traditional multiple linear regression model but enables to model nonlinearity structure. Compared to the neural network models that are often criticized by the requirements of past experience and reliable knowledge in the design of network architecture, the suggested method only involves a few parameter estimates. A regularized algorithm was used to estimate the PFLRM parameters. It is shown that the regularized PFLRM improves the forecast accuracy of power output over the traditional multiple linear regression and neural network models. The results were validated based on a 2.1 kW grid connected PV system.

Evaluation of data driven models for river suspended sediment concentration modeling

Using eight-year data series from hydrometric stations located in Arkansas, Delaware and Idaho (USA), the ability of artificial neural network (ANN) and support vector regression (SVR) models to forecast/estimate daily suspended sediment concentrations ([SS]d) was evaluated and compared to that of traditional multiple linear regression (MLR) and sediment rating curve (SRC) models. Three different ANN model algorithms were tested [gradient descent, conjugate gradient and Broyden–Fletcher–Goldfarb–Shanno (BFGS)], along with four different SVR model kernels [linear, polynomial, sigmoid and Radial Basis Function (RBF)]. The reliability of the applied models was evaluated based on the statistical performance criteria of root mean square error (RMSE), Pearson’s correlation coefficient (PCC) and Nash–Sutcliffe model efficiency coefficient (NSE). Based on RMSE values, and averaged across the three hydrometric stations, the ANN and SVR models showed, respectively, 23% and 18% improvements in forecasting and 18% and 15% improvements in estimation over traditional models. The use of the BFGS training algorithm for ANN, and the RBF kernel function for SVR models are recommended as useful options for simulating hydrological phenomena.

Parameter Automatic Calibration Approach for Neural-Network-Based Cyclonic Precipitation Forecast Models

This paper presents artificial neural network (ANN)-based models for forecasting precipitation, in which the training parameters are adjusted using a parameter automatic calibration (PAC) approach. A classical ANN-based model, the multilayer perceptron (MLP) neural network, was used to verify the utility of the proposed ANN–PAC approach. The MLP-based ANN used the learning rate, momentum, and number of neurons in the hidden layer as its major parameters. The Dawu gauge station in Taitung, Taiwan, was the study site, and observed typhoon characteristics and ground weather data were the study data. The traditional multiple linear regression model was selected as the benchmark for comparing the accuracy of the ANN–PAC model. In addition, two MLP ANN models based on a trial-and-error calibration method, ANN–TRI1 and ANN–TRI2, were realized by manually tuning the parameters. We found the results yielded by the ANN–PAC model were more reliable than those yielded by the ANN–TRI1, ANN–TRI2, and traditional regression models. In addition, the computing efficiency of the ANN–PAC model decreased with an increase in the number of increments within the parameter ranges because of the considerably increased computational time, whereas the prediction errors decreased because of the model’s increased capability of identifying optimal solutions.

Estimating civil aircraft’s research and manufacture cost by using grey system model and neural network algorithm

Purpose – The purpose of this paper is to propose novel civil aircraft cost parameters’ selection method and novel cost estimation approach for civil aircraft so as to effectively simulate or forecast civil aircraft cost under poor information and small sample. Design/methodology/approach – Based on existent cost estimation indexes, this paper summarized civil aircraft research and manufacturing cost impact index system and adopted grey relational model to select most important impact factors. Consider civil aircrafts’ cost information could not be easily collected, the author must estimate their costs with limited sample and poor information. A combination model of GM (0, N) model and BP neural network algorithm is proposed. Both advantages of simulation of BP neural network algorithm and poor information generation of GM (0, N) were effectively combined. Then steps of combined model were given out. Finally, nine types of aircrafts were used to test the validity of proposed model. As comparing with the traditional multiple linear regression model and simple GM (0, N) model, results indicated that proposed model can do the work better. Findings – Grey relational model can be applied for parameters’ selection and combined GM (0, N) model and BP neural network algorithm can estimate aircraft’s cost as well. Results show that novel combined model could get high forecasting accuracy. Practical implications – Cost estimation is key problem in production management of civil aircraft. Effective cost management could promote competitiveness of aircraft manufacturing company. Proposed combined model can be applied for civil aircraft cost estimation. Similarly, it could be applied for other complex equipment cost estimation. Originality/value – The paper succeeds in proposing grey relational model for cost parameters’ selection and constructing a combination model of GM (0, N) model and BP neural network algorithm. Algorithm of the proposed model was discussed and steps were given out.

Modeling Bus Dwell Time with Decision Tree-Based Methods

A large proportion of transit travel time is made up by dwell time for passengers boarding and alighting. More accurate modeling and estimation of bus dwell time (BDT) can enhance the efficiency and reliability of the public transportation system. Multiple linear regression (MLR) has been the most commonly used method in the literature for modeling and estimating BDT. However, the underlying assumptions of the MLR method, such as multicollinearity and normality of random error, cannot always be satisfied for real applications. This study developed and implemented two methods based on decision trees (DTs), namely, classification and regression tree and chi-squared automatic interaction detector, for the first time for BDT modeling and estimation. The models were compared with the traditional MLR model after calibrating and validating the new models against the data collected from four bus stops in Auckland, New Zealand. Various error measurements were used to evaluate the accuracy of the models. The DT-based methods eliminated the limitations of the MLR method and provided reliable and accurate estimation of BDT.

A wavelet‐based multiple linear regression model for forecasting monthly rainfall

ABSTRACTIn this article, a rainfall forecasting model using monthly historical rainfall data and climate indices is developed by incorporating the multi‐resolution analysis (MRA) and multiple linear regression (MLR) model. The monthly rainfall anomaly and large‐scale climate index time series are decomposed using MRA into a certain number of component subseries at different temporal scales. The hierarchical lag relationship between the rainfall anomaly and each potential predictor is identified by cross correlation analysis with a lag time of at least one month at different temporal scales. The components of predictor variables with known lag times are then screened with a stepwise linear regression algorithm to be selectively included into the final forecast model. This MRA‐based rainfall forecasting method is examined with 46 stations over South Australia, and compared to the traditional MLR model based on the original time series. The models are trained with data from the 1959–1995 period and then tested in the 1996–2008 period for each station. The performance is compared with observed rainfall values, and evaluated by common statistics of relative absolute error and correlation coefficient. The results show that the proposed MRA‐based model provides considerably more accurate monthly rainfall forecasts for all of the selected stations over South Australia than the traditional regression model. For the MRA‐based method, historical rainfall is consistently useful for all examined stations, while the large‐scale climate signals are only partly useful for some stations.

A Novel Output Prediction Method in Production Management Based on Parameter Evaluation Using DHNN

Output prediction is one of the difficult issues in production management. To overcome this difficulty, a dynamic-improved multiple linear regression model based on parameter evaluation using discrete Hopfield neural networks (DHNN) is presented. First, a traditional multiple linear regression model is established; this model takes the factors in production lifecycle (not only one phase of the production) into account, such as manufacturing resources, manufacturing process, and product rejection rate, so it makes the output prediction be more accurate. Then a static-improved model is built using the backstepping method. Finally, we obtain the dynamic-improved model based on parameter evaluation using DHNN. These three models are applied to an aviation manufacturing enterprise based on the actual data, and the results of the output prediction show that the models have practical value.

Modelling the Linkage Between Landscape Metrics and Water Quality Indices of Hydrological Units in Sihu Basin, Hubei Province, China: An Allometric Model

Studying quantitative relationships between landscape pattern and water quality is a fundamental step to assess the impacts of non-point source pollution. Many hydrological models with multi-functionality have been developed as useful tools to study several key mechanisms in non-point source pollution. In landscape ecological studies, however, the empirical modelling approaches have been dominated with emphasis on the relationships between the landscape metrics and water quality indices. The main techniques for developing those models of landscape-water quality are statistical regression analysis based on linear models. In this article, Allometric models and the traditional multiple linear regression models for estimating the linkage between landscape metrics and water quality were tested in Sihu Basin, Hubei Province, China. The models at patch class level were established in 24 hydrological units of the basin, which took nine water quality indices (EC, pH, SS, DO, COD, TN, TP, NO3--N, NH4+-N) as the dependent variables and eighteen landscape metrics calculated in FRAGSTATS 3.3 as independent variables. The results suggested that, compared with the traditional multiple linear regression models, Allometric models were more suitable for SS, DO, TP, TN, NH4+-N, in which landscape pattern metrics could explain the 80.5%, 77.7%, 58.2%, 43.9%, 67.6% of total variation, respectively. There had little difference between multiple linear regression models and Allometric models for EC and NO3--N. The coefficients of determination in Allometric models were not as strong as that obtained in the multiple linear regression models for pH and COD. The above results indicated that using Allometric model may potentially provide a new way to study the linkage between landscape metrics and water quality indices, which will help protect our regional water resources.

Applicability of multilayer feed-forward neural networks to model the onset of river breakup

Predicting the onset of breakup is an essential component of any ice jam flood forecasting system, yet it presents a difficult challenge due to the complex nature of the relationship between meteorological conditions, streamflow hydraulics and ice mechanics. For this research, data extracted from historical hydrometric and meteorological records were used to develop and assess a three-layer feed-forward artificial neural network (ANN) model for predicting the onset of breakup, using the Hay River in northern Canada as the demonstration site. The calibration results illustrate the potential of the ANN model for successful forecasting of the onset of river ice breakup, i.e. the first transverse cracking of the ice cover. However, rigorous validation also indicates that the accuracy of such ANN models can be optimistically overestimated by their performance during the calibration phase. The possible reasons for this poor predictive capability of the ANN model are also discussed. Despite this caveat, the proposed model shows improved performance as compared to the more conventional multiple linear regression (MLR) techniques typically applied to this problem. ► Illustrates a feed-forward ANN model for forecasting the onset of river breakup. ► Model performance is demonstrated for the Hay River, NWT, Canada. ► ANN model out-performs traditional multiple linear regression models. ► ANN model is validated using the leave-one-out-cross-validation method.

An accurate nonlinear QSAR model for the antitumor activities of chloroethylnitrosoureas using neural networks

The quantitative structure–activity relationship (QSAR) studies are investigated in a series of chloroethylnitrosoureas (CENUs) acting as alkylating agents of tumors by neural networks (NNs). The QSAR model is described inaccurately by the traditional multiple linear regression (MLR) model for the substitution of CENUs at N-3, whose characteristics play key roles in the biological activity. A nonlinear QSAR study is undertaken by a three-layered NN model, using molecular descriptors that are known to be responsible for the antitumor activity to optimize the input variables of the MLR model. The results demonstrate that NN models present the relationship between antitumor activity and molecular descriptors clearly, and they yield predictions in excellent agreement with the experiment's obtained values ( R 2 = 0.983). The R 2 value is 0.983 for the 5-8-1 NN model, compared with 0.506 for the MLR model, and the nonlinear model is able to account for 98.3% of the variance of antitumor activities.

Forecasting daily pollen concentrations using data-driven modeling methods in Thessaloniki, Greece

Abstract Airborne pollen have been associated with allergic symptoms in sensitized individuals, having a direct impact on the overall quality of life of a considerable fraction of the population. Therefore, forecasting elevated airborne pollen concentrations and communicating this piece of information to the public are key issues in prophylaxis and safeguarding the quality of life of the overall population. In this study, we adopt a data-oriented approach in order to develop operational forecasting models (1–7 days ahead) of daily average airborne pollen concentrations of the highly allergenic taxa: Poaceae, Oleaceae and Urticaceae. The models are developed using a representative dataset consisting of pollen and meteorological time-series recorded during the years 1987–2002, in the city of Thessaloniki, Greece. The input variables (features) of the models have been optimized by making use of genetic algorithms, whereas we evaluate the performance of three algorithms: i) multi-Layer Perceptron, ii) support vector regression and iii) regression trees originating from distinct domains of Computational Intelligence (CI), and compare the resulting models with traditional multiple linear regression models. Results show the superiority of CI methods, especially when forecasting several days ahead, compared to traditional multiple linear regression models. Furthermore, the CI models complement each other, resulting to a combined model that performs better than each one separately. The overall performance ranges, in terms of the index of agreement, from 0.85 to 0.93 clearly suggesting the potential operational use of the models. The latter ones can be utilized in provision of personalized and on-time information services, which can improve quality of life of sensitized citizens.

Hypothesis testing in functional linear regression models with Neyman's truncation and wavelet thresholding for longitudinal data

Longitudinal data sets in biomedical research often consist of large numbers of repeated measures. In many cases, the trajectories do not look globally linear or polynomial, making it difficult to summarize the data or test hypotheses using standard longitudinal data analysis based on various linear models. An alternative approach is to apply the approaches of functional data analysis, which directly target the continuous nonlinear curves underlying discretely sampled repeated measures. For the purposes of data exploration, many functional data analysis strategies have been developed based on various schemes of smoothing, but fewer options are available for making causal inferences regarding predictor-outcome relationships, a common task seen in hypothesis-driven medical studies. To compare groups of curves, two testing strategies with good power have been proposed for high-dimensional analysis of variance: the Fourier-based adaptive Neyman test and the wavelet-based thresholding test. Using a smoking cessation clinical trial data set, this paper demonstrates how to extend the strategies for hypothesis testing into the framework of functional linear regression models (FLRMs) with continuous functional responses and categorical or continuous scalar predictors. The analysis procedure consists of three steps: first, apply the Fourier or wavelet transform to the original repeated measures; then fit a multivariate linear model in the transformed domain; and finally, test the regression coefficients using either adaptive Neyman or thresholding statistics. Since a FLRM can be viewed as a natural extension of the traditional multiple linear regression model, the development of this model and computational tools should enhance the capacity of medical statistics for longitudinal data.