A gardener wants to determine the daily amount of water required to maximize the height of her tomato seedlings. She has 50 pots, one tomato seed in each. She randomly assigns each pot to a certain amount of water (in mL/day). After 3 weeks, she measures the seedlings’ heights (in cm). These data are recorded in the file tomato. csv. You may assume that heights are independent and normally distributed with common SD. a. (2 marks) Write down a linear regression model to describe these data. Include both linear and quadratic functions of the predictor variable. Be sure to define your variables and to state all assumptions. b. (1 mark) Why is your model in (a), which contains a quadratic function of the predictor variable, considered a linear model? c. (1 mark) Fit the model and provide the table of parameter estimates and their standard errors. d. (2 marks) Provide a scatterplot of the data superimposed with the fitted regression function. e. (1 mark) Which daily amount of water do you recommend to maximize the height of the seedlings? (You can approximate this value using your plot in (d) or use calculus to get a more exact answer.) f. (1 mark) Provide the coefficient of determination. g. (1 mark) Provide the sample correlation between seedling height and daily amount of water h. (2 marks) The coefficient of determination and the sample correlation are both measures of association between height and water. Explain why, in this context, one of these values is relatively high and other relatively low tomato water height 20 0 20 0 20 7.8 20 0.4 20 0.6 40 24.6 40 18.3 40 9.7 40 12.6 40 13.8 60 34.1 60 29.8 60 30 60 28.6 60 25.2 80 44.9 80 38.5 80 26.2 80 39.5 80 33.6 100 34.7 100 38.9 100 34.9 100 36.4 100 36.9 120 31.6 120 44.2 120 40.8 120 34.3 120 46.3 140 38.1 140 34.5 140 40.5 140 40.4 40.5 140 40.4 140 40.1 160 31.4 160 30.8 160 27.7 160 26.5 160 26.1 180 12.5 180 15 180 9.7 180 26.8 180 22 200 0 200 0 200 0 200 3.9 200 0