intermediate Business Statistics assignments

-

BAFN 305 - Multiple Regression Questions

The attached provides descriptive statistics, correlations and a multiple regression run for four variables.

The four variables are about corporate earnings, debt, sales and ownership. Sample size is 400

companies. You are provided means, standard deviations, correlations and two regression models, a full

and reduced model.

The variables are: Earnings per share (EPS) - the 'Y'variable-\, Company Debt, measured in millions of dollars,

Annual Sales, measured in millions of US dollars, and

Public or private ownership, a binary of (1,0) with 1 assigned to public.

Answer the following:

L. What percent of the companies are private. How many is that 2. The best predictor of EPS is 3. The weakest predictor of EPS is 4. ldentify the independent variable(s) understudy 5. A multiple regression model for EPS = f(Debt Sales,Ownership] was run and is noted on the

attached. Answer the following:

a. Coefficient of determination is b.TestthehypothesisthatHop=0'AIphaat.05(AcceptorReject}-

a. State the critical value b. State the computed value c. State the p-value d. State the decision e. State the conclusion.

c. State the regression equation to forecast EPS.

d. Test the hypothesis to determine the importance of each variable. a. State the critical value for the test - Alpha at .01 TT b. State the computed value and the p-value for each

c. State the decisions.

d. State the conclusions.

6. lf you completed the above, you evaluated the 'Full Model' a. Would you create a reduced model based on the analysis above. b. lf so, which variables would be kept for the reduced model. c. lf you ran the reduced model, why did you remove the variable, multicollinearity or lack

of a relationship with 'Y'.

d. Would the model provide good prediction of EPS._ Why

7

Full Model - Earnings = f(Debt,Sales,Ownership)

Summary

R-Square .75

Standard error .75 Cases 400

Reduced Model - Earnings = f(Debt, Sales)

Summary R-Square .71

Standard error .80 Cases 400

Earnings (per sh) Debt Sales Public/Private(1,0

Means 3.00 20 (million) 30 (million) .65

Standard Deviations 1.50 8 (million) 10 (million) .30

Correlations Earnings Debt Sales Public/Private(t,0) Earninss 1.00 Debt -.58 1.00

Sales 0.40 0.40 1.00

Public/Private (1,0) 0.30 =.25 o.41 1.00

ANOVA Sum of squares Df Mean Square F p-value

Regression 7,500 3 2.s00 396.20 .000

Residual 2.s00 396 6.31 Total 10,000 399

Variable Coefficient Standard Error t/z statistic p-value lntercept 1.25 Debt -.10 xxxxxxxx -2.70 .006 Sales 0.15 xxxxxxxx L.45 .090

Public/Private 0.08 xxxxxxxx L.40 .096

ANOVA Sum of squares Df Mean Square F p-value

Reeression 7,too 2 3s50 486.30 .000 Residual 2,9OO 397 7.30

Total 10,000 399

Variable Coefficients Standard error t/z statistic lntercept 1.85 Debt -.L4 xxxxxxxx -2.90 .003 Sales .20 xxxxxxxx 2.00 ,o23