Q2. [10 pts] Simple Linear regression: An economist conducted a study of the possible association between...

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Q2. [10 pts] Simple Linear regression: An economist conducted a study of the possible association between weekly income and weekly grocery expenditures. The particular interest was whether higher income would result in shoppers spending more on groceries. A random sample of shoppers at a local supermarket was obtained, and a questionnaire was administered asking about the weekly income of the shopper's family and the grocery bill for that week. The gender of the shopper was also obtained. The summary data below is based on expenditures and income for 10 selected survey participants. Variable Weekly income Sample Mean 553.200 Weekly grocery expenditure 105.900 Sample STD, s 309.043 37.867 In addition, the correlation between weekly income and weekly grocery expenditure is 0.649. (a) [1 pt] Which variable is the response variable, weekly income, or weekly grocery expenditure? (b) [2 pts] Fit a least-square line to the data, determine the intercept, a, and the slope, b based on the given information. Round your results up to 4 decimal places. (c) [2 pts] If the weekly income increases by $100, what is the amount change in the weekly grocery bill? Show details of your calculation. Round your results up to 4 decimal places. (d) [2 pts] Find the predicted weekly grocery expenditure when the weekly income is $2000. (e) [3 pts] Calculate one measure and assess how good is the model fit to the data. Is this least-square line an effective model to the data? Why? 1 Q2. [10 pts] Simple Linear regression: An economist conducted a study of the possible association between weekly income and weekly grocery expenditures. The particular interest was whether higher income would result in shoppers spending more on groceries. A random sample of shoppers at a local supermarket was obtained, and a questionnaire was administered asking about the weekly income of the shopper's family and the grocery bill for that week. The gender of the shopper was also obtained. The summary data below is based on expenditures and income for 10 selected survey participants. Variable Weekly income Sample Mean 553.200 Weekly grocery expenditure 105.900 Sample STD, s 309.043 37.867 In addition, the correlation between weekly income and weekly grocery expenditure is 0.649. (a) [1 pt] Which variable is the response variable, weekly income, or weekly grocery expenditure? (b) [2 pts] Fit a least-square line to the data, determine the intercept, a, and the slope, b based on the given information. Round your results up to 4 decimal places. (c) [2 pts] If the weekly income increases by $100, what is the amount change in the weekly grocery bill? Show details of your calculation. Round your results up to 4 decimal places. (d) [2 pts] Find the predicted weekly grocery expenditure when the weekly income is $2000. (e) [3 pts] Calculate one measure and assess how good is the model fit to the data. Is this least-square line an effective model to the data? Why? 1