Question

In: Statistics and Probability

You run a regression analysis using Data Analysis to answer the following question: Is stock selling price a function of annual dividend?

SUMMARY OUTPUT
Regression Statistics
Multiple R 0.818616296
R Square 0.67013264
Adjusted R Square 0.658351663
Standard Error 9.16867179
Observations 30
ANOVA
df SS MS F Significance F
Regression 1 4781.80995 4781.80995 56.8826 3.2455E-08
Residual 28 2353.807187 84.06454239
Total 29 7135.617137
Coefficients Standard Error t Stat P-value Lower 95% Upper 95%
Intercept 28.21496731 3.739591617 7.544932763 3.22E-08 20.55476114 35.87517349
Dividend 2.367177613 0.313863719 7.542055589 3.25E-08 1.724256931 3.010098296
c. You run a regression analysis using Data Analysis to answer the following question: Is stock selling price a function of annual dividend?
     The Regression output table is to the right. Is the overall model statistically significant? State how you made your decision.
g. Interpret the coefficient of determination (r2)
e. What are the regression coefficients for the independent variable and the constant from the table?
b0:
b1:
f.   Interpret the regression coefficients.
b0:
b1:
g. Write the regression equation using the regression coefficient and constant.
h.   What is the predicted price per share of a stock for a company that gives an annual dividend of $18?

Solutions

Expert Solution

c) To check whether overall model is statistically significant we perform F test

Test statistic , F = 56.8826

The P value for F with (1,28) df is less than 0.0001 (the significance F )

Since P value is very small , we can conclude that the overall model is significant

d) Coefficient of determination , r2 = 0.6701

That means 67.01% variation in stock selling price can be explained the model .

e) b0 = 28.21497 (constant /y- intercept )

b1= 2.36718 (coefficient of independent variable, dividend / slope )

f) b0 , which is the y intercept , is the value of y when x=0 . In the context of the problem $28.21  is the stock selling price when annual dividend is zero.

y intercept may not have any practical meaning most of the time , but it has mathematical significance.

b1: the slope , for each unit increase in independent variable (annual dividend) , the independent variable increases by $2.37 on an average .

g) The equation of line of regression is

Stock selling price = 28.21 + 2.37 * Annual dividend

h) Predicted price per share of a stock = 28.21 + 2.37* 18

= $70.87

g)

W


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