In: Statistics and Probability
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? |
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)
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