Question

(4) A regression software output is given below. df ANOVA Source Regression Residual Total 4 SS 227,09 153,07 380,16 MS 56,8 6,1 25 29 Variables Intercept X1 X2 X3 X4 Standard Coefficients Error 68,33 8,9 0,85 0,3 -0,33 0,8 -0,81 0,2 -0,58 0,2 a. How large is the sample size? b. Write the regression equation. Interprete the coefficient of X2. c. Determine and interprete the coefficient of determination. d. Conduct a global test of hypothesis fort he meaning of the regression equation. Use the .01 significance level e. Conduct an individual test of hypothesis on each of the independent variables. Would you consider dropping any of the independent variables? Use the 0.01 significance level.

Answer 1

Solution-A:

sample size,n=dftotal+1=29+1=30

Solution-B:

y^=68.33+0.85x1-0.33x2-0.81x3-0.58x4

coefficient of x2=-0.33

Holding x1,x3 constant,for unit increase in x1,y decreases by 0.33 on an average

Solution-c:

Rsq=1-SS reg/SS total

=1-(227.09/380.16)

=0.4026463

=0.4026463*100

=40.26% variation in y is explained by model

Expalined variance by model=40.26%

Solution-d:

Ho:beta1=beta2=beta3=0

Ha:Atleast one of the beta is not =0

alpha=0.01

F=MS regression/MS total

=56.8/6.1

=9.311475

p value in excel

=F.DIST.RT(9.311475,4,25)

=9.46761E-05

=0.0000946

p<0.01

Reject Ho

Accept Ha

There is suffcient statistical evidence at 1% level of signiifcance to conclude that there is a linear relatiosnhip between y and indpendent variables

Overall regression model is signifcant

we can use this model for predicting from x1,x2 ,x3 and x4