Needs to Done on Time!!!

For each of the two majors:

Draw the scatter diagram of Y = ‘Annual % ROI’ against X = ‘Cost’.

Solution:

The scatter diagram of Y =”Annual % ROI against X=Cost is as follows:

Obtain b0 and b1 of the regression equation defined as y ̂ = b0 + b1X and the coefficient of determination (r2) from the Excel regression output.

Solution:

The regression output is as follows:

From the above result we get b0=0.1268 and b1=-2E-07

Hence the regression equation is =-2E-07* X+0.1268

The coefficient of determination (r2) is 0.9515

Draw the fitted regression line on the scatter diagram.

Solution:

The fitted regression line on the scatter diagram is as follows:

Calculate the estimated ‘Annual % ROI’ when the ‘Cost’ (X) is $160,000.

Solution:

Estimated Annual % ROI when Cost (X) is $160,000

Annual % ROI=0.1268-2E-07*$160000=0.0148=1.48%

Test the hypothesis:

H0: β1 = 0

Ha: β1 ≠ 0

Solution:

Null hypothesis H0: β1 = 0 Vs Ha: β1 ≠ 0

The test statistics will be t test and test statistics is t=

Under the null hypothesis t=

From the regression output in the above we get t corresponding to Cost (X) =-18.7849 and the corresponding P value is 2.83396E-13.

Since the P value corresponding to t=-18.7849 is 2.83396E-13 which is less than 0.05 at 5% level of significance therefore we reject the null hypothesis that β1 = 0.

Write a paragraph or more on any observations you make about the regression estimates, coefficient of determination, the plots, and the results of your hypothesis tests

Solution:

From the above result we have seen that the estimated regression equation is =-2E-07* X+0.1268 and the coefficient of determination of the regression line is 0.9515 which means the regression model explains 95.15% variation of the total variation and model is the best model to predict future observation, we have also seen from hypothesis test that Cost (X) is significant to the model and from the scatter plot we have seen that there is a strong correlation between Cost (X) and Annual % ROI.

For “Business Major” Excel sheet:

For each of the two majors:

Draw the scatter diagram of Y = ‘Annual % ROI’ against X = ‘Cost’.

Solution:

The scatter diagram of Y =”Annual % ROI against X=Cost is as follows:

Obtain b0 and b1 of the regression equation defined as y ̂ = b0 + b1X and the coefficient of determination (r2) from the Excel regression output.

Solution:

The regression output is as follows:

From the above result we get b0=0.118 and b1=-2E-07

Hence the regression equation is =-2E-07* X+0.118

The coefficient of determination (r2) is 0.941

Draw the fitted regression line on the scatter diagram.

Solution:

The fitted regression line on the scatter diagram is as follows:

Calculate the estimated ‘Annual % ROI’ when the ‘Cost’ (X) is $160,000.

Estimated Annual % ROI when Cost (X) is $160,000

Annual % ROI=0.118-2E-07*$160000=0.006=0.6%

Test the hypothesis:

H0: β1 = 0

Ha: β1 ≠ 0

Solution:

Null hypothesis H0: β1 = 0 Vs Ha: β1 ≠ 0

The test statistics will be t test and test statistics is t=

Under the null hypothesis t=

From the regression output in the above we get t corresponding to Cost (X) =-16.9475 and the corresponding P value is 1.64456E-12.

Since the P value corresponding to t=-16.9475 is 1.64456E-12which is less than 0.05 at 5% level of significance therefore we reject the null hypothesis that β1 = 0.

Write a paragraph or more on any observations you make about the regression estimates, coefficient of determination, the plots, and the results of your hypothesis tests

Solution:

From the above result we have seen that the estimated regression equation is

y ̂=-2E-07* X+0.118 and the coefficient of determination of the regression line is 0.941 which means the regression model explains 94.1% variation of the total variation and model is the best model to predict future observation, we have also seen from hypothesis test that Cost (X) is significant to the model and from the scatter plot we have seen that there is a strong correlation between Cost (X) and Annual % ROI.

Scatter Diagram

Cost(X)

Annual ROI

Scatter Diagram

Cost (X)

Annula ROI

Scatter Diagrram

Cost (X)

Annual ROI

Scatter Diagram

Cost (X)

Annual ROI

SUMMARY OUTPUT

Regression Statistics

Multiple R0.9754

R Square0.9515

Adjusted R Square0.9488

Standard Error0.0033

Observations20

ANOVA

dfSSMSFSignificance F

Regression10.0038543410.003854341352.87377652.83396E-13

Residual180.0001966091.09227E-05

Total190.00405095

CoefficientsStandard Errort StatP-valueLower 95%Upper 95%Lower 95.0%Upper 95.0%

Intercept0.12680.00202084362.737191761.56075E-220.1225363790.1310276460.1225363790.131027646

Cost (X)-2E-071.14214E-08-18.784934832.83396E-13-2.38545E-07-1.90554E-07-2.38545E-07-1.90554E-07

SUMMARY OUTPUT

Regression Statistics

Multiple R0.970

R Square0.941

Adjusted R Square0.938

Standard Error0.003

Observations20

ANOVA

dfSSMSFSignificance F

Regression10.0021617260.002161726287.22067761.64456E-12

Residual180.0001354747.52636E-06

Total190.0022972

CoefficientsStandard Errort StatP-valueLower 95%Upper 95%Lower 95.0%Upper 95.0%

Intercept0.1180.00242949348.586213791.51456E-200.1129357010.1231440520.1129357010.123144052

Cost (X)-2E-071.24622E-08-16.947586191.64456E-12-2.37386E-07-1.85022E-07-2.37386E-07-1.85022E-07