Question

i. Use MS Excel Data Analysis ToolPak to perform a multiple regression analysis using Quality as the response variable and Helpfulness and Clarity as the explanatory variables. Write down the corresponding coefficient estimates and provide the regression output.

j. Perform an F-test for the overall usefulness of the model in part i) using a 5% significance level. Make sure you follow all the steps for hypothesis testing indicated in the Instructions section and clearly state your conclusion.

k. Test manually if the Clarity variable is significant in the model in part i). Make sure you follow all the steps for hypothesis testing indicated in the Instructions section and clearly state your conclusion.

l. Using the adjusted R² criterion, does including Clarity as an additional predictor variable improve the model in part i)? Explain why it is better to use the adjusted R² over the R² to determine if the addition of this new variable improves the model.

Regression Statistics			ANOVA
Multiple R	0.998544859			df	SS	MS	F	Significance F
R Square	0.997091836		Regression	2	255.2639136	127.6319568	62229.00058	0
Adjusted R Square	0.997075813		Residual	363	0.744514614	0.002051004
Standard Error	0.045288017		Total	365	256.0084282
Observations	366
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%	Lower 95.0%	Upper 95.0%
Intercept	-0.020353502	0.010520921	-1.934574223	0.0538193	-0.04104311	0.000336106	-0.04104311	0.000336106
helpfulness	0.538358378	0.007216008	74.60611907	2.8925E-222	0.524167949	0.552548808	0.524167949	0.552548808
clarity	0.465505241	0.00707634	65.78333849	8.6445E-204	0.451589474	0.479421009	0.451589474	0.479421009

Answer 1

## Q i )  Use MS Excel Data Analysis ToolPak to perform a multiple regression analysis using Quality as the response variable and Helpfulness and Clarity as the explanatory variables. Write down the corresponding coefficient estimates and provide the regression output.

y = Quality  and x1 = helpfulness   and x2 = clarity

Quality = β0 + (β1 *x1) + (β2 * x2) ie

here coefficint for intercept is     -0.020353502

and coefficient for helpfullness is 0.538358378 and coefficient for clarity 0.465505241

Quality = -0.020353502 + (0.538358378* x1) + (0.465505241* x2)

here intercept is - 0.020353502 and

slope 1 is 0.538358378 : it is postive as x1 value increases y value increases

slope 2 is 0.465505241 : it is positve as x2 value increases y value increases .

### Q j )  Perform an F-test for the overall usefulness of the model in part i) using a 5% significance level. Make sure you follow all the steps for hypothesis testing indicated in the Instructions section and clearly state your conclusion.

step 1 ) To test : Ho : overall regression model is not significant vs H1 : overall model is significant .

step 2) test statistics : F = 62229.01408

step 3) p value = 0

step 4) decision : we rejct Ho if p value is less than alpha value using p value approach here p value is less than alpha value we reject Ho .

step 5) conclusion : there is enough evidence to conclude that the overall model is significant at given level of significance .

## Q k.) Test manually if the Clarity variable is significant in the model in part i). Make sure you follow all the steps for hypothesis testing indicated in the Instructions section and clearly state your conclusion.

## test for helpfulness : coefficent of x1 :

step 1) to test : β1 = 0 vs H1 : β1 ≠ 0

step 2) test statistics = t = 74.60611907

step 3) p value = 0

step 4) decision : we reject Ho if p value is less than alpha value using p value approach here p value is less than alpha value we reject Ho

step 5) conclusion : there is enogh evidence to conclude that coefficient of x1 is significant at given level of significance .

## test for clarity : coefficent of x2 :

step 1) to test : β2 = 0 vs H1 : β2 ≠ 0

step 2) test statistics = t = 65.78333849   

step 3) p value = 0

step 4) decision : we reject Ho if p value is less than alpha value using p value approach here p value is less than alpha value we reject Ho

step 5) conclusion : there is enough evidence to conclude that coefficient of x2 is significant at given level of significance .

## Q l )  Using the adjusted R2 criterion, does including Clarity as an additional predictor variable improve the model in part i)? Explain why it is better to use the adjusted R2 over the R2 to determine if the addition of this new variable improves the model.

Answer : R squre ( coefficient of determination ) and Adjusted R square value both have value is greater than 0.90

that is variation explained by model is very very good

if we use or consdier Adjusted R sqaure value it is very very good .

## using adjusted R2 criterion, does including Clarity as an additional predictor variable improve the model in part i

yes , it does including Clarity as an additional predictor variable improve the model in part i

and clarity coefficient is also significant hence it include in the model .

## Explain why it is better to use the adjusted R2 over the R2 to determine if the addition of this new variable improves the model.

because here R square and Adjusted R square value is very very good , so if we use addition of new variable improves the model . here in this case the Adjusted R squared compansates for the addition of variables and only increase if the new predictor enhances the model above .