# Use hand calculations to fit the multiple linear regression model 1 y = Î²0 + Î²1x1 + Î²2x2 to the

## Question:

y = Î²0 + Î²1x1 + Î²2x2

to the data set in DS 13.6.2.

(a) Write down the vector of observed values of the response variable Y and the design matrix X.

(b) Calculate X'X.

(c) Verify that

(d) Verify that Î²^0 = 4, Î²^1 = -3, and Î²^2 = 1.

(e) Calculate the vector of predicted values of the response variable Y and the vector of residuals e.

(f) What is the sum of squares for error?

(g) Show that the estimate of the error variance is Ïƒ^2 = 54/7.

(h) What is the standard error of Î²^1? Of Î²^2? Should either of the input variables be dropped from the model?

(i) What is the fitted value of the response variable when

x1 = 2 and x2 = -2?

What is the standard error of this fitted value?

(j) Construct a 95% prediction interval for a future value of the response variable obtained with x1 =2 and x2 = -2.

Future value (FV) is the value of a current asset at a future date based on an assumed rate of growth. The future value (FV) is important to investors and financial planners as they use it to estimate how much an investment made today will be worth...

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**Related Book For**

## Probability And Statistics For Engineers And Scientists

**ISBN:** 9780495107576

3rd Edition

**Authors:** Anthony Hayter

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