question 6

FP-Q.6 ( 7 marks) Corrina is conducting a study of how sleep and GPA are related. She surveys the students in her statistics class and creates a table comparing hours of sleep to GPA. The survey data are presented in the following table. Sloop GPA 4 (4.2 5 6.5 7 7.6 3.1 3.2 8.4 8.5 9 9.5} 2.5'27 3 3.2 3.3 3.4 3.5 3.4 3.5 3.5 3.9 3.7 The R code below uses the variable Sleep to store the number of hours of sleep, while GPA comprises student GPA. # Hours of sleep S1eep=c(4, 4.2, 5, 6.5, 7, 7.6, 8.1, 8.2, 8.4, 8.5, 9, 9.5) # GPA GPA=c( 2.5, 2.7, 3, 3.2, 3.3, 3.4, 3.5, 3.4, 3.5, 3.5, 3.9, 3.7) Important Note: In parts (a), (b) and (c), student should use R (or Rstudio) to answer. For each of these parts, your answer should include the R code, the R output and the comment of the R output. (a) Draw the scatterplot of the data using GPA as dependent variable and Hours of sleep independent variable. How would you describe the trend in the data? (0.75 mark) (b) Compute the linear correlation coefcient. Interpret its value in the context of the problem. (0.75 mark) (C) Fit the simple linear regression with Number of hours of sleep (Sleep) as the independent variable (X) and GPA as the dependent variable (y). (0.5 mark) ((1) From the Routput in (c), write down the least squares regression equation. (0.5 mark) (9) Interpret the meaning of the slope of regression line in the context of problem. (0.5 mark) (f) Test, at the 10% level of significance, the hypothesis that the slope of the population regression line is different from 0, against the null hypothesis that it is exactly 0. Report the value of the t-test statistic, the degrees of freedom, the p-value and your conclusion. (1.5 marks) (g) Calculate a 95% confidence interval for the population slope. (1 mark) (h) Find and interpret the coefficient of determination. (1 mark) (i) Estimate the GPA of a student who sleep 10 hours. 0.5 mark) 2