Exercise: MLR 2 Using Regression in the Data Analysis Add-in of Excel (or other

Question

Exercise: MLR 2 Using Regression in the Data Analysis Add-in of Excel (or other suitable software), answer the following questions by fitting a linear equation to the following data (Y, X1, X2, X3) (4540,30250,99,1732), (3000,28960,97,1541), (3368,28675,85,1522), (3700,29720,100,1682), (4115,29710,101,1642). Regress Y on all three X variables. Given Question(s) 1. From the Excel output, what is u? Answer: u3 (Unitless) 2. From the Excel output, what is v? Answer: v = 1 (Unitless) 3. From the Excel output, what is Fts? (Unitless) (Answer Length = 4) Score My Answer Practice Investigate 4. From the Excel output, what is the p-value for Ft? 5. Is the overall relationship significant? The null hypothesis is that a significant linear relationship DOES NOT exist between the dependent variable and the independent variables. Test the null hypothesis using a significance level of 0.01. Enter 1 for REJECT THE NULL HYPOTHESIS, 2 for FAIL TO REJECT THE NULL HYPOTHESIS 6. From the Excel output, what is the p value for 7. I.po equal to 0 at a significance level of 0.05? The null hypothesis is that it equals 0. Enter 1 for REJECT THE NULL HYPOTHESIS, 2 for FAIL TO REJECT THE NULL HYPOTHESIS. 8. From the Excel output, what is the p-value for 9. Is B3 equal to 0 at a significance level of 0.1? The null hypothesis is that it equals 0. Enter 1 for REJECT THE NULL HYPOTHESIS, 2 for FAIL TO REJECT THE NULL HYPOTHESIS

Explanation / Answer

Lets first populate the table into Excel and run the data analysis. The output from the analysis is as below

1. From the Output U=3 stands for the degrees of freedom of Regression (k). This is one less than the number of variables, here we have 4 variable so degree of freedom is 3.

2. V =1 is the degree of freedom for the Residual/ Error. This is calculated by the formula n-k-1, so here it is n=5, k=3, n-k-1 = 5-3-1= 1

3. The Fts value for the regression 6.737

4. The p value for Fts is 0.274268, this indicates the significance of the F calculated.

5. Regression analysis is testing the Null Hypothesis

H0: 1 = 2 = ... = k = 0

Against
H1: At least one is not zero

The null hypothesis states that there is no significant relationship between the variables i.e all are zero's.

The alternative hypothesis assumes that every independent variable has an impact on the dependent variable or atleast one of the independent variable has an impact on the dependent variable.

Regression analysis runs an ANOVA to calculate the significance of the relationship of the variable and P value of the F statistic indicates the significance level. If the p value is less than 0.05 we reject the Null Hypothesis else we do not reject the Null Hypothesis.

Here the P value is 0.274268 which is greater than 0.05 so we FAIL TO REJECT THE NULL HYPOTHESIS. Here the overall relationship is significant. Hence the answer is 2

6. The excel output for p value of 0 is 0.294746

7. Here the 0 value is -51072.6 which is not equal to zero. The p value for 0 is 0.27476 which is greater than 0.05 so we FAIL TO REJECT THE NULL HYPOTHESIS. Hence the answer is 2

8. The excel output for p value of 3 is 0.516369

7. Here the 3 value is -8.60431 which is not equal to zero. The p value for 0 is 0.516369 which is less than 0.1(here the value indicates 10% or 0.1 level of significance). so we REJECT THE NULL HYPOTHESIS. Hence the answer is 1

ANOVA df SS MS F Significance F Regression 3 1398890 466296.6 6.737099 0.274268 Residual 1 69213.27 69213.27 Total 4 1468103 Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0% Intercept -51072.6 25494.07 -2.00331 0.294746 -375005 272860.3 -375005 272860.3 X1 2.534566 1.407399 1.800886 0.322696 -15.3481 20.41727 -15.3481 20.41727 X2 -61.0693 34.03256 -1.79444 0.323666 -493.494 371.3554 -493.494 371.3554 X3 -8.60431 9.058566 -0.94985 0.516369 -123.704 106.4957 -123.704 106.4957

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