The prices (in $) of Domestic, Inc. stock ( y ) over a period of 12 days, the nu
ID: 3224773 • Letter: T
Question
The prices (in $) of Domestic, Inc. stock (y) over a period of 12 days, the number of shares (in 100s) of company's stocks sold (x1), and the volume of exchange (in millions) on the New York Stock Exchange (x2) are shown below.
Day
(y)
(x1)
(x2)
1
87.50
950
11.00
2
86.00
945
11.25
3
84.00
940
11.75
4
83.00
930
11.75
5
84.50
935
12.00
6
84.00
935
13.00
7
82.00
932
13.25
8
80.00
938
14.50
9
78.50
925
15.00
10
79.00
900
16.50
11
77.00
875
17.00
12
77.50
870
17.50
df
SS
MS
F
Significance F
Regression
2
118.8474
59.4237
40.9216
0.0000
Residual
9
13.0692
1.4521
Total
11
131.9167
Coefficients
Standard Error
t Stat
P-value
Intercept
118.5059
33.5753
3.5296
0.0064
(x1)
-0.0163
0.0315
-0.5171
0.6176
(x2)
-1.5726
0.3590
-4.3807
0.0018
a.
Use the output shown above and write an equation that can be used to predict the price of the stock.
b.
Interpret the coefficients of the estimated regression equation that you found in Part a.
c.
At a .05 level of significance, determine which variables are significant and which are not.
d.
If on a given day, the number of shares of the company that were sold was 94,500 and the volume of exchange on the New York Stock Exchange was 16 million, what would you expect the price of the stock to be?
Day
(y)
(x1)
(x2)
1
87.50
950
11.00
2
86.00
945
11.25
3
84.00
940
11.75
4
83.00
930
11.75
5
84.50
935
12.00
6
84.00
935
13.00
7
82.00
932
13.25
8
80.00
938
14.50
9
78.50
925
15.00
10
79.00
900
16.50
11
77.00
875
17.00
12
77.50
870
17.50
Explanation / Answer
a.Use the output shown above and write an equation that can be used to predict the price of the stock.
the regression equation that can be used to predict
y = a + b1x1 + b2x2
From the table coefficents corresponding to
b0 = intercept = 118.5059
b1 : coeffecient (x1) = -0.0163
b2 : Coefficent (x2) = -1.5726
So the equation to predict the price of the stock
y = 118.5059 -0.0163x1 -1.5726x2
(b) Interpret the coefficients of the estimated regression equation that you found in Part a.
As the coefficients of x1,x2 are negative,
if x1 ( : the number of shares (in 100s) of company's stocks sold (x1)) increases the y: value of the stock decreases by 0.0163 times when there were no change in x2 :the volume of exchange (in millions) on the New York Stock Exchange (x2)
Similarly x2 : :the volume of exchange (in millions) on the New York Stock Exchange (x2) the y: value of the stock decreases by 1.5726 times when there were no change in x1 ( : the number of shares (in 100s) of company's stocks sold (x1))
c .
Null hypothesis : H0: b0 =0(Coefficient of interccept is not significant) ; and the ccorresponding p-value is 0.0064 as this p-value is less than 0.05; we reject null hypothesis; the b0 is not equal to 0. so the intercept coefficent is significant.
Null hypothesis : H0: b1 =0(Coefficient of x1 is not significant) ; and the ccorresponding p-value is 0.6716 as this p-value is greater than 0.05; we accept null hypothesis; the b1 is equal to 0. so the coefficent of x1 is not significant.
Null hypothesis : H0: b2 =0(Coefficient of x2 is not significant) ; and the ccorresponding p-value is 0.0018 as this p-value is less than 0.05; we reject null hypothesis; the b2 is not equal to 0. so the coefficent of x2 is significant.
d.If on a given day, the number of shares of the company that were sold was 94,500 and the volume of exchange on the New York Stock Exchange was 16 million, what would you expect the price of the stock to be?
x1 = the number of shares (in 100s) of company's stocks sold (x1) = 94500/100 = 945
x2 = volume of exchange (in millions) on the New York Stock Exchange (x2) =16
Substitute these values in the equation to predict the value of y: price of the stock
y = 118.5059 -0.0163x1 -1.5726x2
y = 118.5059 - 0.0163 x 945 - 1.5726 x 16 = 118.5059 - 15.4035 - 26.1616 = 118.5059 - 40.5651=77.9408
Expected price of the stock to be = 77.9408
Coefficients Standard Error t Stat P-value Intercept 118.5059 33.5753 3.5296 0.0064 (x1) -0.0163 0.0315 -0.5171 0.6176 (x2) -1.5726 0.359 -4.3807 0.0018Related Questions
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