Question 2 In a study of the relationship between X = mean daily temperature for the...

Question 2

In a study of the relationship between X = mean daily temperature for the month and Y = monthly charges on the electrical bill the following data was gathered:

Temperature (^oF): X_i	16	28	13	22	25	19
Number of Calls: Y_i	95	120	70	115	130	85

We are interested in fitting the following simple linear regression model: Y = Xβ + ε

a) Calculate X′X, (X′X)^-1 and X′Y and then calculate the least squares estimates of β₀ and β_1.

b) Calculate the variance-covariance matrix of b, and use it to perform a t-test to test the null hypothesis that β₁ = 0. Use α = 0.05.

Use the matrix approach to calculate the following:

c) Calculate a 95% confidence interval for the mean of Y when X = 20.

d) Calculate a 95% prediction interval for an individual new value of Y when X = 20.

Expert Solution

orchestra answered 1 year ago

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