Consider the example of a credit card company that has a database of information provided by its customers when they apply for credit cards. An analyst has created a multiple regression model for which the dependent variable in the model is credit card charges accrued by a customer in the dataset over the past year (y), and the independent variables are the customer's annual household Income (x1), number of members of the household (x;), and number of years of post-high school education (X3). Click on the datale logo to reference the data. DATA- (a) (b) (6) Estimate the con'espondlng simple linear regression with the customer's annual household income as the Independent variable and credit card charges accrued by a customer over the past year as the dependent variable. X1 represents customer's annual household income. If required, round your answers to three decimal places. For subtractive or negative numbers use a minus sign even If there Is a + sign before the blank. (Example: -300) 5' = + x1 Interpret the estimated relationship between the customer's annual household income and credit card charges accrued over the past year. Choose the correct answer below. (i) As a customer's annual income decreases by $1000, the credit card charges accrued by the customer over the past year will be higher. (ll) As a customer's annual Income Increases by $1000, the credit card charges accrued by the customer over the past year will be higher. (iii) As a customer's annual income increases by $1000, the credit card charges accrued by the customer over the past year will be lower. (iv) As a customer's annual income decreases by $1000, the credit card charges accrued by the customer over the past year will be lower. How much variation In credit card charges accrued by a customer over the past year Is explained by this simple linear regression model? If required, round your answer to two decimal places. % Estimate the corresponding simple linear regression with the number of members in the customer's household as the independent variable and credit card charges accrued by a customer over the past year as the dependent variable. X2 represents number of members of the household. If required, round your answers to three decimal places. For subtractive or negative numbers use a minus sign even if there is a + sign before the blank. (Example: -300) Interpret the estimated relationship between the number of members in the cusmmer's household and credit card charges accrued over the past year. Choose the correct answer below. (i) As the number of members in the customer's household decreases by one, the credit card charges accrued by the customer over the past year will be higher. (ii) As the number of members in the customer's household increases by one, the credit card charges accrued by the customer over the past year will be lower. (iii) As the number of members in the customer's household increases by one, the credit card charges accrued by the customer over the past year will be higher. (iv) As the number of members in the customer's household decreases by one, the credit card charges accrued by the customer over the past year will be lower. How much variation in credit card charges accrued by a customer over the past year is explained by this simple linear regression model? If required, round your answer to two decimal places. 0In Estimate the corresponding simple linear regression with the customer's number of years of post-high school education as the independent variable and credit card charges aocrued by a customer over the past year as the dependent variable. X: represents number of years of posthigh school education. If required, round your answers to three decimal places. For subtractive or negative numbers use a minus sign even if there is a + sign before the blank. (Example: -300) 9 . . x. Interpret the estimated relationship between the customer's number of years of post-high school education and credit card charges aocrued over the past year. Choose the correct answer below. (i) As a customer's years of posthigh school education increases by one year, the credit card charges accrued by the customer over the past year will be lower. (ll) As a customer's years of post-high school education decreases by one year, the credit card charges accrued by the customer over the past year will be lower. (iii) As a customer's years of post-high school education decreases by one year, the credit card charges accrued by the customer over the past year will be higher. (iv) As a customer's years of posthigh school education increases by one year, the credit card charges accrued by the customer over the past year will be higher. How much variation in credit card charges accrued by a customer over the past year is explained by this simple linear regression model? If required, round your answer to two decimal places. % (d) Consider the multiple regressions with credit card charges accrued by a customer over the past year as the dependent variable and customer's annual household income (x1), number of members of the household (x2), and number of years of post-high school education (X3) as the independent variables. 5" = 2051.639 + 120.632Xl + 533.346x2 - 505.632x3 Do the estimated slopes differ substantially from the corresponding slopes that were estimated using simple linear regression in parts (a), (b), and (c)? What does this tell you about multicollinearity in the multiple regression model shown above? The input in the box below will not be graded, but may be reviewed and considered by your instructor. blank (e) Consider the multiple regressions with credit card charges accrued by a customer over the past year as the dependent variable and customer's annual household income (X1), number (f) of members of the household (X2), and number of years of post-high school education (X3) as the independent variables. The coefcient of determination for the multiple regression model ls 36.35%. Y = 2051.639 + 120.63ZX1 + 533.846X2 - 505.632X3 Add the coefcients of determination for the simple linear regression In parts (a), (b), and (c), and compare the result to the coefcient of determination for the multiple regression model shown above? What does this tell you about multicollinearity in the multiple regression model shown above? The input in the box below will not be graded, but may be reviewed and considered by your instructor. blank Add age, a dummy variable for sex, and a dummy variable for whether a customer has exceeded his/her credit limit in past 12 months as independent variables to the multiple regression model shown in part (d). Code the dummy variable for sex as 1 if the customer is female and 0 if male, and code the dummy variable for whether a customer has exceeded his/her credit limit In past 12 months as 1 If the customer has exceeded his/her credit limit In the past 12 months and 0 otherwise. Do these variables substantially Improve the fit of your model? elect your answer Explain. The Input In the box below will not be graded, but may be reviewed and considered by your Instructor. blank