a. Write out the null and alternative hypotheses to test for a positive linear relationship, using correct notation, between Balance and Monthly Income.

b. Should the null hypothesis be rejected? Report the value of the test statistic and show how you reached your decision. (Use ? = 0.05).

c. State the estimated regression equation.

d. Interpret B?1 , the slope of the regression line and, if appropriate, ?B?0 the intercept, in the context of the question.

e. Use the estimated linear regression line to estimate the average monthly credit card Balance of credit card holders with monthly incomes of $4,000. (Show your working)

f. Interpret the R-squared value in the context of the question.

g. Write which assumption/s about the residuals of regression is/are being tested and comment on whether or not the/these assumption/s hold.

h. Is the multiple linear regression model better than the simple linear regression model at explaining monthly credit card balances? (Comment on R-square value)

i. Comment on the significance and sign of the coefficients for Monthly_Income, Gender, Goldcard, Rewards, and Savings in the multiple regression model and if appropriate interpret the coefficients in the context of monthly credit card balances.

Data:

Scatter Plot of Balance by Monthly_Income R2 Linear = 0.227 $6,000 O 800 co O O $4,000 Balance C $2,000 8 0 8 $0 $0 $2,000 $4,000 $6,000 $8,000 $10,000 Monthly_IncomeRegression Variables Entered/Removeda Variables Variables Model Entered Removed Method Monthly_Inco Enter me D a. Dependent Variable: Balance b. All requested variables entered. Model Summary" Adjusted R Std. Error of Model R R Square Square the Estimate 476 227 226 $955.034 a. Predictors: (Constant), Monthly_Income b. Dependent Variable: Balance ANOVA Sum of Model Squares df Mean Square F Sig. Regression 227171445.2 1 227171445.2 249.067 <.001b residual total a. dependent variable: balance b. predictors: monthly_incomecoefficients standardized unstandardized coefficients model b std. error beta sig. monthly_income .384 .476 variables entered removed method savings enter rewards gender gold monthly_inco me d all requested entered. summary adjusted r of square the estimate .373 balanceanova sum squares df mean f regression sig .236 .030 .292 .335 o oo predicted value>