Question

# The estimated regression equation for a model involving two independent variables and 55 observations is: y-hat...

The estimated regression equation for a model involving two independent variables and 55 observations is:

y-hat = 55.17 + 1.1X1 - 0.153X2

Other statistics produced for analysis include:

SSR = 12370.8

SST = 35963.0

Sb1 = 0.33

Sb2 = 0.20

1. Interpret b1 and b2 in this estimated regression equation

b. Predict y when X1 = 55 and X2 = 70.

1. Compute R-square and Adjusted R-Square.

e. Compute MSR and MSE.

f. Compute F and use it to test whether the overall model is significant using a p-value (α = 0.05).

g. Perform a t test using the critical value approach for the significance of β1.

Use a level of significance of 0.05.

h. Perform a t test using the critical value approach for the significance of β2.

Use a level of significance of 0.05.

a)-: Interpretation of b1= If X2 is fixed, then for each change of 1 unit in X1 , y changes 1.1 units.

Interpretation of b2= If X1 is fixed, then for each change of 1 unit in X2 , y changes (- 0.153) units.

b)-: X1 = 55 X2 = 70

put value of X1 and X2 in estimated regression equation then ,

y-hat = 55.17 + (1.1)*55 + ( - 0.153)*70 = 104.91

c)-: R - square = SSR/SST = 12370.8/35963 = 0.3439 = R^2

adjusted R- sqaure = k = number of independent variable = 2

n = number of observation = 55

adjusted R - square = 1- (1 - 0.3439)*[54/52] = 0.215

e) -: MSR = SSR/df(r) df(r) = degree of freedom regression = k - 1 = 2 - 1 = 1

df(e) = df(total) - df(r) = 54 - 1 = 53 [ df(total) = n - 1 = 54]

MSR = 12370.8

SST = SSR + SSE -->    SSE = SST - SSR = 35963 - 12370.8 = 23592.2 ; SSE = 23592.2

MSE/df(e) = 23592.2/53 = 445.13

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