Data for a random sample of four individuals are presented in the Table below. The data relates the individual's age to the number of hours he typically sleeps per night.

X Y

10 10

20 8

30 8

40 6

(Y=Sleep in hours)

(X=Age in years)

Assume a simple regression model = + +

(a)State your a priori assumptions about ₀₁.

(b)Obtain the equation of the least squares line (Use Microsoft Excel). Interpret the numerical values of the regression coefficients.

(c)State the required conditions for the error variable.

(d)What is the estimate of the error variance?

(e)What is r² and interpret the meaning of this number?

(f)Test at a significance level of 5% if the simple regression model is significant. Discuss the results of your tests. Is there enough statistical evidence to conclude that the number of hours an individual sleeps is related to the age of the individual?

Provide a 95% prediction interval for the number of hours of slept by an individual that is 37 years old. Interpret this interval.