(b) A teacher wants to develop a multiple linear regression model to predict happiness index (Y) by the number of hours

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B A Teacher Wants To Develop A Multiple Linear Regression Model To Predict Happiness Index Y By The Number Of Hours 1 (162.78 KiB) Viewed 28 times

(b) A teacher wants to develop a multiple linear regression model to predict happiness index (Y) by the number of hours spent on doing exercise (X₁) and the number of working hours (X2). She randomly selected a sample of 60 working adults for this study. These selected adults were asked to fill in a questionnaire on happiness index, the number of hours spent on doing exercise per week and the number of working hours per week. The scores of happiness index range from 0 to 100. Higher score indicates that the working adult feels happier. A multiple linear regression model was then developed by R using this data set and the outputs are shown below. Variable Name in R Description Happy Happiness index (Y) Exercise Number of hours spent on doing exercise per week (X₁) Number of working hours per week (X₂) Working > summary (MRmodel) Cal 1m (formula = Happy ~ Exercise + Working, data = happydata) Coefficients: Estimate Std. Error t value Pr(> [t]) 1.54E-06 (Intercept) 3.5178 0.7481 4.702 Exercise 4.6237 0.9177 5.038 8.72E-07 Working -2.4863 1.6895 -1.472 0.0249 > anova (MRmodel) Analysis of Variance Table Response: Happy Df F value Pr (>F) Sum Sq Mean Sq 532.4 Exercise 1 532.4 5.7254 0.0467125 Working 1 1123.6 1123.6 19.4253 0.0005891 Residuals 57 3275.3 57.5 (i) Find the estimated multiple linear regression equation for predicting the happiness index of the working adults based on the above R output. Perform the significance test for the model parameter of the number of hours spent on doing exercise X₁ with level of significant of 0.01. (6 marks) Calculate the adjusted coefficient of determination. Correct the final answer to 4 decimal places. (2 marks)