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
orchestra answered 3 years agoRelated Solutions
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x y
71.2 23.1
90.8 122.9
88.8 82.9
57.7 18.3
71.4 8.6
60.4 25.9
60.2 -43.1
88.5 77.4
68.2 -5.9
41.1 -83
61.4 -2.5
87.1 39.4
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Number of Promotions
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3
2554
2
1746
11
2755
14
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4
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SAT Score
GPA
670
1.2
720
1.8
750
2.3
845
1.9
960
3.0
1,000
3.3
1,180
3.2
1,200
3.4
1,370
2.9
1,450
3.8
1,580
4.0
1,600
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a) Run a regression analysis on the following bivariate set of data with y as the...
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data with y as the response variable.
x
y
10.7
81.6
13.7
81.5
36.7
56.5
4
72.1
50.7
23.2
47.6
-4.8
37.3
31.9
24.3
75.2
21.5
59.3
17.2
54.6
23.6
75.5
22.2
60.8
29.3
51
14
63.4
0.2
102.7
30.7
48.2
10.3
74.8
26.5
48.2
23.1
87
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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%
Intercept
-1931.41991
243.9210071
-7.918218817
9.39705E-11
-2419.863299
CPI
8.914424548
1.13956563
7.822651293
1.35489E-10
6.632483736
Nasdaq
0.020174909
0.005420724
3.721810856...
8. Run a regression analysis on the following bivariate set of data with y as the...
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data with y as the response variable.
x
y
27.2
68.2
28.1
66.7
28.7
64.6
30.2
66.4
33.7
69.5
31.8
68.3
30.4
67.8
28.6
65.5
32.5
69.4
34.8
67.9
33.3
67.1
28
66.1
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r =
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explained by the variation in the values of x? Report
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Run a regression analysis on the following bivariate set of data with y as the response...
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with y as the response variable.
x
y
15.5
58.8
25.4
62.9
53.7
68.8
46.5
78.6
28.5
57.5
5.7
68.1
-0.4
67.8
43.8
87.7
23.1
64.9
31.3
81.3
48.2
80.1
15.9
71.1
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2) What proportion of the variation in y can be
explained by the variation in the values of x? Report
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Run a regression analysis on the following bivariate set of data with y as the response...
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x
y
81
81.3
92.6
90.8
80.1
94.9
77.8
53.4
89.4
102.9
70.3
38.2
90.2
98
81.4
94.6
94.9
122.4
77.2
42.1
70.6
47.8
71
50.6
Find the correlation coefficient and report it accurate to three
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r =
What proportion of the variation in y can be explained by
the variation in the values of x? Report answer as a
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Run a regression analysis on the following bivariate set of data with y as the response...
Run a regression analysis on the following bivariate set of data
with y as the response variable.
x
y
73
16.1
80
14.9
72.5
8.5
55.8
33.6
54.6
23.4
76.6
26.2
74.6
19.1
40.2
40.6
58.7
25.8
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What proportion of the variation in y can be explained by
the variation in the values of x? Report answer as a
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