4. Can the speed of a vehicle be predicted by the age of its driver? The speeds Y (in km/h) of a sample of ten vehicles are recorded, along with the ages X of their drivers. From the data, we...

Extracted text: 4. Can the speed of a vehicle be predicted by the age of its driver? The speeds Y (in km/h) of a sample of ten vehicles are recorded, along with the ages X of their drivers. From the data, we calculate i = 48.2, j = 107.8, (z:-2)² = 3669.6, (4- û)° = 752.7. The least squares regression line is calculated to be ŷ = 133.198 – 0.527x. It is also determined that 57.5% of the variation in the speed of a vehicle can be accounted for by its regression on the age of the driver. (a) What is the value of the correlation between the age of a driver and the speed of a vehicle? (b) Provide an interpretation of the slope of the least squares regression line. (c) Calculate a 95% confidence interval for the parameter 31 in the simple linear regression model. (d) We would like to conduct a hypothesis test at the 5% level of significance to determine whether a linear relationship exists between the age of a driver and the speed of a vehicle. Could the confidence interval in (c) have been used to conduct the test? Why or why not? If it could be used, what would the conclusion be, and why?