Dependent Variable: Y | R-Square | F-Ratio | p-Value on F Observations: 18 | 0.3

Question

Dependent Variable: Y | R-Square | F-Ratio | p-Value on F

Observations: 18 | 0.3066 | 7.076 | 0.0171

Variable: Parameter Estimate | Standard Error | TRatio /P Values

Intercept: 15.48 | 5.09 | 3.04/0.0008

x: -21.36 | 8.03 | -2.66/0.0171

Question

A. What is the equation of the sample regression line?

B. How many degrees of freedom does this regression analysis have?

C. Test the intercept and slope estimates for statistical significance at the 1 percent significance level. Explain how you performed this test and present your results.

D. What does the parameter estimate of b indicate?

E. What does the parameter estimate of a indicate?

F. If X = 20, what is the predicted value of Y?

G. Test the overall equation for statistical significance at the 1 percent significance level. Explain how you perform this test and present your results.  Interpret the p-value for the F-statistic.

H. What does the value of R-SQUARE indicate?

Explanation / Answer

1.The estimated Regression Equation is given by : Y = 15.48 -21.36X

2.This regression has N-1 degree of freedom .That is 18 -1 = 17.

3.The rule for testing the significance is : If P-value < level of significance , reject null hypothesis and accept Alternate Hypothesis . And IF p-vALUE > Level of significance accept null hypothesis and reject alternate hypotheis ...WHere Null hypothesis = H0 = beta coefficients =0

H1 =beta coefiicients is not equal to zero

In our case we have for Intercept P- value = 0.0008 < 0.01

Hence we reject Null hypothesis and accept alternate hypothesis ..This Implies that the intercept coefficient is significant.

And for the Slope coefiicient The P- value is given by 0.0171 which is greater than 0.01.Hence we accept null hypothesis and reject alternate hypotheisis.Hence we can say that the slope coefficient is insignificant at 1 % level of significance.

D. The parameter estimate of b indicate that for a 1 unit increase in x there will be 21.36 decrease in the value of Y.However at 1 % level of signifance when we performed hypothesis testing we come to know that this beta coefiicient is insignificant and is not to be considered in this particular model.

hence our model becomes y =15.48

E.The parameter estimate that the intercept of this regression function is 15.48 i.e If X =0,we will have Y =15.48.

F.iF x = 20 ,THE PREDICTED VALUE OF Y is still 15.48

G.Overall significane of any regression model is always checked with the help of F -test and the Null hypothesis in this case is given by H0 = beta1 = 0 and beta2 = 0

Alternate Hypothesis : Atleast one of beta coefficient the is not Zero

Where F test =( R^2 /(K-1)) / (1-R^2)/(N-K)

= (0.3066/(2-1)) / (1-0.3066) /(18-2) = 0.3066/0.04333375 = 7.074

This is F-Calculated.We have search for F-Critical in the F-table .If F critical is less than F-calculated we reject null hypothesis and accept alternate hypothesis And Vice Versa.Please see the F-table for Degree of freedom 1 for numerator and 16 for denominater and find F-crital value.The P-value on F is given as 0.0171

This is your critical F-value which is smaller than the calculated F-value ,hence you reject null hypothesis..

H.R-squared is a statistical measure of how close the data are to the fitted regression line. It is also known as the coefficient of determination.

R-squared = Explained variation / Total variation = 0.3066 .This implies 30.66 % of the variation in Y is explained by the regression model.

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