You run a regression analysis

SUMMARY OUTPUT
Regression Statistics
Multiple R 0.818616296
R Square 0.67013264
Adjusted RSquare 0.658351663
Standard Error 9.16867179
Observations 30
ANOVA
df SS MS F SignificanceF
Regression 1 4781.80995 4781.80995 56.8826 3.2455E-08
Residual 28 2353.807187 84.06454239
Total 29 7135.617137
Coefficients StandardError t Stat P-value Lower95% Upper95%
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 aregression analysis using Data Analysis to answer the followingquestion: Is stock selling price a function of annualdividend?
     TheRegression output table is to the right. Is the overall modelstatistically significant? State how you made your decision.
g. Interpret thecoefficient of determination (r2)
e. What are theregression coefficients for the independent variable and theconstant from the table?
b0:
b1:
f.  Interpret the regression coefficients.
b0:
b1:
g. Write theregression equation using the regression coefficient andconstant.
h.  What is the predicted price per share of a stock for a company thatgives an annual dividend of $18?

Answer:

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

Test statistic , F = 56.8826

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

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

d) Coefficient of determination , r2 = 0.6701

That means 67.01% variation in stock selling price can beexplained 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 stockselling 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 onan 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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