A nutritionist is conducting a study to understand how a person's calorie intake changes over a period of time. The independent variable X is the number of weeks into the program. This ranges from 1 to 500, representing each week of the program. The dependent variable Y is the calorie intake of each volunteer. The nutritionist aims to use regression analysis to understand if there a trend in calorie intake over the weeks and if the number of weeks in the program be used to predict a volunteer's calorie intake. The sample dataset and plot of relationship between week and calorie intake are provided below. Calrie Intake 400 350 300 250 200 150 100 50 0 0 56; 149 4; 88 20; 62 72; 193 80; 167 52; 118 100 Week 168 296 503 392 80 56 352 444 168; 272 200 4 20 228 475 Table 1: Sample Dataset 228; 319 168; 192 200 Calorie Intake 272 311 186 365 167 200; 229 149 366 310 229 88 62 319 275 296; 311 300 Week 352; 366 392; 365 428; 300 400 444; 310 475; 275 482; 202 500 503; 186 Figure 1: Relationship between week and calorie intake (You can see x and y values respectively corresponding to each data point in the plot) 600 a) Which regression model is appropriate for this dataset? Explain the reason. (5 pt) b) Formulate the regression model that you choose in part a. (5 pt) c) Estimate parameters of the regression model using the sample data given in Table 1. (10 pt) d) Based on your estimated regression function, what are the predicted calorie intake for the weeks 4, 228, 475, 352 and 80? (5 pt) e) Calculate standardized residuals for the data values given in part d. (Take = 31.83) (10 pt) f) Decide if these 5 data values outliers or not. How do you decide? (5 pt)