Question

Using the following Multiple Regression Analysis, Answer the questions (Show all work).

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.988681823
R Square	0.977491746
Adjusted R Square	0.976307101
Standard Error	10.49117857
Observations	61
ANOVA
	df	SS	MS	F	Significance F
Regression	3	272454.9563	90818.31876	825.1347922	6.64497E-47
Residual	57	6273.695181	110.0648277
Total	60	278728.6514
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%	Lower 95.0%	Upper 95.0%
Intercept	-1931.41991	243.9210071	-7.918218817	9.39705E-11	-2419.863299	-1442.976516	-2419.863299	-1442.976516
CPI	8.914424548	1.13956563	7.822651293	1.35489E-10	6.632483736	11.19636536	6.632483736	11.19636536
Nasdaq	0.020174909	0.005420724	3.721810856	0.000454545	0.009320096	0.031029721	0.009320096	0.031029721
Inflation	-54.2455964	5.404007141	-10.03803196	3.27142E-14	-65.06693402	-43.42425873	-65.06693402	-43.42425873

a. Using the F-value, determine if the slope of at least one of the predictors in your model is not equal to 0. Based on the F-value, should you proceed to interpret results for the individual predictor variables in your model? Why or Why not?

b. Assuming that your F-value indicated that you could proceed with interpreting results for individual predictor variables, which variable (s) in your model was a significant predictor of LMT's stock price (Intercept)?

c. How much variance in LMT's stock price (Intercept) is shared by the 3 predictor variables? Based on these results, are the 3 predictor variables useful in predicting LMT's stock prices? Why or Why not?

Answer 1

a) Null Hypothesis: All the slope of the predictors are zero in the model.

Against

Alternative Hypothesis: The slope of at least one of the predictors in your model is not equal to 0.

Here the calculated F statistic for the regression model is

F=825.1347922

The F critical Value at 5% level of significance with (3,57) degrees of freedom is =3.355

Here 825.1347922 > 3.355

Therefore we reject the null hypothesis at 5% level of significance with (3,57) degrees of freedom.

Hence the slope of at least one of the predictors in your model is not equal to 0.

We can not interpret results for the individual predictor variables in the model based on the F- values. Since the F statistics does not test the significance of individual slopes. We need to go for t test.

b) Here all the variables that is CPI, Nasdaq and inflation are significant predictor of LMT's stock price in the model since the pvalue for the t test are less than the 5% level of significance.

c) 97.75% of variability in LMT's stock price is explained by the three predictor variable. Therefore we conclude that the model best fits the data.Therefore predictor variables useful in predicting LMT's stock prices.