3. A mail-order company collected data on 150 customers and wanted to understand current year spending amounts. Data were collected on the following variables: - Log(AmountSpent) - the logarithm of annual expenditure, in - Age - age of the customer, in years - Gender - reported gender of the customer, male =1 and female =0 - Married - customer's marital status, married =1 and otherwise =0 - Salary - customer's household salary, in - Children - number of children in the household. Results of a multiple regression involving the above variables is: (a) State the estimated regression equation and comment on R2. (4 marks) (b) Assess the overall significance of the model, as well as the significance of the individual regression coefficients. Use a 1% significance level for each test. (6 marks) (c) Explain why the estimated coefficient of the salary variable is so small relative to the other estimated coefficients. (4 marks) (d) Calculate an approximate 90% confidence interval for the logarithm of annual expenditure for a 28-year-old married female with no children with an annual salary of 55,000. Use a t coefficient of 1.656. (5 marks) (e) Discuss, with brief reasons, what changes you would recommend making to the above regression model. (6 marks) 3. A mail-order company collected data on 150 customers and wanted to understand current year spending amounts. Data were collected on the following variables: - Log(AmountSpent) - the logarithm of annual expenditure, in - Age - age of the customer, in years - Gender - reported gender of the customer, male =1 and female =0 - Married - customer's marital status, married =1 and otherwise =0 - Salary - customer's household salary, in - Children - number of children in the household. Results of a multiple regression involving the above variables is: (a) State the estimated regression equation and comment on R2. (4 marks) (b) Assess the overall significance of the model, as well as the significance of the individual regression coefficients. Use a 1% significance level for each test. (6 marks) (c) Explain why the estimated coefficient of the salary variable is so small relative to the other estimated coefficients. (4 marks) (d) Calculate an approximate 90% confidence interval for the logarithm of annual expenditure for a 28-year-old married female with no children with an annual salary of 55,000. Use a t coefficient of 1.656. (5 marks) (e) Discuss, with brief reasons, what changes you would recommend making to the above regression model. (6 marks)
