Question

Thefollowingdatarelatethespeedofaparticulartypistandthetemper-

ature setting of his office. The units are words per minute and degrees Fahrenheit.

Temperature

50 60 70

Typing speed

63 74 79

(a) Compute,byhand,thevalueofSSR.

(b) Estimate σ 2 .

(c) Ifthetemperatureissetat65,whattypingspeedwouldyoupredict?

Answer 1

(a)

These are the data that have been provided for the dependent and independent variables:

Obs.	X	Y
1	50	63
2	60	74
3	70	79

Now, with the provided sample values of the predictor and the response variable, we need to construct the following table to compute the estimated regression coefficients:

Therefore, the regression equation is:

Now that we have the regression equation, we can compute SSR​. The regression sum of squares is computed as follows:

Hence, the regression sum of squares is SSR​=128.

(b)

(c)

When X = 65 then