The Excel file Age SleepHoursxlsx contains information recorded on a random sample of 39 individuals. The file contains Sleep (in Hours) per night and Age (in year) for each person. Download the data file and fit a linear regression model for predicting sleep hours (Y) from age (X). Use your Excel output, and any other information provided, to answer the following questions. For each question, either choose the most correct option, or type in the answer to the number of decimal places specified. Flgura 1 Figuraz a C! ' h a In. (D a 3 ' 22; o E 0 .. ., all In. In N O 05 0.0 0.5 1.0 20 40 60 80 Residuds Age Figure 3 0.5 Residuals U D -O.5 Age in years Answer the following questions by choosing the most correct option or typing the answer: 1. {3 marks) The assumptions for a linear model that need to be investigated (choose the figure that goes with each statement): 0 Linearity assumption can be checked by looking at the relationship between sleep hours and age : 8 0 Whether the residuals are drawn from a normal distribution X 0 X 0 Whether the residuals have a constant standard deviation across the range of ages 2. {1 mark) The highest age had the highest sleep hours c X For the remaining questions you may assume that any relevant assumptions have been met 3. {1 mark) The slope of the least squares regression line is : x 4. {2 marks) The age with the largest residual had sleep hours equal to 7.207 and age of 25. Calculate the value of the residual. Type the absolute value of the residual with 3dp X 5. {2 marks) The absolute value of the test statistic for testing the slope of the regression line is: X [3dp) with degrees of freedom equal to: X (integer). 6. (1 mark) The pivalue for testing the slope of the regression line is less than 0.05. X 7. {2 marks) Select the most appropriate conclusion to the question "Is the age [in years) a useful predictor for sleep hours?". Choose one of the following: c X A: There is a significant negative linear relationship between Sleep Hours and Age. B: There is not enough evidence to indicate that Age is a useful predictor of SleepHours. C: There is a significant positive linear relationship between SleepHours and Age. 8. {1 mark) The correlation is: X (3dp remember to include a negative sign if appropriate) 9. {2 marks) Use the regression equation to predict the sleep hours for a person who is 22 years old {3dp}: X 0 10. {1 marks) We are 95% confident that for each extra year of age, the average sleep hours is expected to 11. {2 mark) The value of the width of the 95% confidence interval (Hint: Upper Limit Lower Limit) is X [3dp)