Regression problem I need help with question 5 and question 6. Many variables in
ID: 3059361 • Letter: R
Question
Regression problem
I need help with question 5 and question 6.
Many variables influence the price of a company’s common stock, including company-specific internal variables such as product quality and financial performance, and external market variables such as interest rates, exchange rates and stock market performance.
The attached table contains quarterly data on three such external variables (x1, x2, and x3) and the price y of Ford Motor Company’s common stock (adjusted for stock splits). The Japanese yen exchange rate, x1, measures the strength of the yen versus the US dollar. The higher the rate, the cheaper are Japanese imports – such as the automobiles of Toyota, Nissan, Honda, and Subaru – to US consumers.
Similarly, the higher the deutsche mark exchange rate, x2, the less expensive are BMW’s and Mercedes Benz’s to US consumers. Finally, the S&P 500 Index, x3, is a general measure of the performance of the market for stocks in US firms.
y is the DV and x1, x2, x3 are the IV.
1) Fit the regression model y = to the data. Report the regression estimates and all the relevant statistics (t-statistics, p-ratio).
2) Explain the ANOVA results and find the coefficient of determination and interpret its value.
3) Do the data provide sufficient evidence that the price of Ford stock is affected by the yen? Reach your conclusion using .
4) Do the data provide sufficient evidence that the price of Ford stock is explained by the deutsche mark ? Reach your conclusion using .
5) Do the data provide sufficient evidence that the price of Ford stock respond to general market conditions? Reach your conclusion using .
6) Is there any evidence of multicollinearity? (Hint: Find the correlation coefficients between any two IVs)
Date
Ford stock Price y
Japanese Yen x1
Deutsche Mark x2
S&P500 x3
1992.1
38.3
133.2
1.64
407.36
1992.2
45.2
125.5
1.53
408.21
1992.3
39.4
119.2
1.41
418.48
1992.4
42
124.7
1.61
435.64
1993.1
52.3
121
1.61
450.16
1993.2
55.3
110.1
1.69
447.29
1993.3
64.7
105.2
1.62
459.24
1993.4
58.1
111.3
1.73
465.34
1994.1
59
103.4
1.76
463.21
1994.2
27.6
99
1.6
454.83
1994.3
27.5
98.5
1.55
466.96
1994.4
26.3
99.6
1.38
455.19
1995.1
29.5
89.4
1.39
493.15
1995.2
31.2
84.6
1.42
539.23
1995.3
28.7
98.2
1.43
578.32
1995.4
28.9
102.4
1.48
614.57
1996.1
34.8
106.3
1.52
647.05
1996.2
36.2
109.8
1.58
668.53
1996.3
32.1
110.5
1.61
672.92
1996.4
31.9
112.6
1.67
689.32
(1)
Report:
Multiple linear regression analysis-
Japanese Yen X1
The test statistic is t = -0.05 and the corresponding P-value
Is P – value = 0.962
Deutsche Mark X2
The test statistic is t = 3.50 and the corresponding P – value
Is P – value = 0.003
S&P 500 X3
The test statistic is t = -2.21 and the corresponding P – value
Is P – value = 0.042
(2)
The Anova results and the coefficient of determination is
Rsqured = SSR/SST
= 1599.26/2818.11
=0.567493817
Rsquared is approx. to 0.5675
the coefficient of determination is Rsquared is 0.5675
Interpretation –
The vavalue of Rsquared = 56.75% of the variation in the dependent variable, Ford stock price can be explained by the independent variables Japanese Yen (X1), Deutsche Mark (X2), and S&P 500 (X3)
(3)
The Ford stock price (Y) is not affected by the Yen, because the t – value is – 0.05 and the corresponding P – value is 0.932 > alpha = 0.05. We do not reject the null hypothesis H0.
(4)
The stock price (Y) is affected by the Deutsche Mark because the t – value is 3.50 and the corresponding p -value is 0.003 < alpha = 0.005. We reject the null hypothesis H0.
(5)
Do the data provide sufficient evidence that the price of Ford stock respond to general
market conditions
(6)
Is there any evidence of multicollinearity?
Date
Ford stock Price y
Japanese Yen x1
Deutsche Mark x2
S&P500 x3
1992.1
38.3
133.2
1.64
407.36
1992.2
45.2
125.5
1.53
408.21
1992.3
39.4
119.2
1.41
418.48
1992.4
42
124.7
1.61
435.64
1993.1
52.3
121
1.61
450.16
1993.2
55.3
110.1
1.69
447.29
1993.3
64.7
105.2
1.62
459.24
1993.4
58.1
111.3
1.73
465.34
1994.1
59
103.4
1.76
463.21
1994.2
27.6
99
1.6
454.83
1994.3
27.5
98.5
1.55
466.96
1994.4
26.3
99.6
1.38
455.19
1995.1
29.5
89.4
1.39
493.15
1995.2
31.2
84.6
1.42
539.23
1995.3
28.7
98.2
1.43
578.32
1995.4
28.9
102.4
1.48
614.57
1996.1
34.8
106.3
1.52
647.05
1996.2
36.2
109.8
1.58
668.53
1996.3
32.1
110.5
1.61
672.92
1996.4
31.9
112.6
1.67
689.32
Explanation / Answer
Regression problem
I need help with question 5 and question 6.
Many variables influence the price of a company’s common stock, including company-specific internal variables such as product quality and financial performance, and external market variables such as interest rates, exchange rates and stock market performance.
The attached table contains quarterly data on three such external variables (x1, x2, and x3) and the price y of Ford Motor Company’s common stock (adjusted for stock splits). The Japanese yen exchange rate, x1, measures the strength of the yen versus the US dollar. The higher the rate, the cheaper are Japanese imports – such as the automobiles of Toyota, Nissan, Honda, and Subaru – to US consumers.
Similarly, the higher the deutsche mark exchange rate, x2, the less expensive are BMW’s and Mercedes Benz’s to US consumers. Finally, the S&P 500 Index, x3, is a general measure of the performance of the market for stocks in US firms.
y is the DV and x1, x2, x3 are the IV.
1) Fit the regression model y = to the data. Report the regression estimates and all the relevant statistics (t-statistics, p-ratio).
2) Explain the ANOVA results and find the coefficient of determination and interpret its value.
3) Do the data provide sufficient evidence that the price of Ford stock is affected by the yen? Reach your conclusion using .
4) Do the data provide sufficient evidence that the price of Ford stock is explained by the deutsche mark ? Reach your conclusion using .
5) Do the data provide sufficient evidence that the price of Ford stock respond to general market conditions? Reach your conclusion using .
6) Is there any evidence of multicollinearity? (Hint: Find the correlation coefficients between any two IVs)
Date
Ford stock Price y
Japanese Yen x1
Deutsche Mark x2
S&P500 x3
1992.1
38.3
133.2
1.64
407.36
1992.2
45.2
125.5
1.53
408.21
1992.3
39.4
119.2
1.41
418.48
1992.4
42
124.7
1.61
435.64
1993.1
52.3
121
1.61
450.16
1993.2
55.3
110.1
1.69
447.29
1993.3
64.7
105.2
1.62
459.24
1993.4
58.1
111.3
1.73
465.34
1994.1
59
103.4
1.76
463.21
1994.2
27.6
99
1.6
454.83
1994.3
27.5
98.5
1.55
466.96
1994.4
26.3
99.6
1.38
455.19
1995.1
29.5
89.4
1.39
493.15
1995.2
31.2
84.6
1.42
539.23
1995.3
28.7
98.2
1.43
578.32
1995.4
28.9
102.4
1.48
614.57
1996.1
34.8
106.3
1.52
647.05
1996.2
36.2
109.8
1.58
668.53
1996.3
32.1
110.5
1.61
672.92
1996.4
31.9
112.6
1.67
689.32
(1)
Report:
Multiple linear regression analysis-
Japanese Yen X1
The test statistic is t = -0.05 and the corresponding P-value
Is P – value = 0.962
Deutsche Mark X2
The test statistic is t = 3.50 and the corresponding P – value
Is P – value = 0.003
S&P 500 X3
The test statistic is t = -2.21 and the corresponding P – value
Is P – value = 0.042
(2)
The Anova results and the coefficient of determination is
Rsqured = SSR/SST
= 1599.26/2818.11
=0.567493817
Rsquared is approx. to 0.5675
the coefficient of determination is Rsquared is 0.5675
Interpretation –
The vavalue of Rsquared = 56.75% of the variation in the dependent variable, Ford stock price can be explained by the independent variables Japanese Yen (X1), Deutsche Mark (X2), and S&P 500 (X3)
(3)
The Ford stock price (Y) is not affected by the Yen, because the t – value is – 0.05 and the corresponding P – value is 0.932 > alpha = 0.05. We do not reject the null hypothesis H0.
(4)
The stock price (Y) is affected by the Deutsche Mark because the t – value is 3.50 and the corresponding p -value is 0.003 < alpha = 0.005. We reject the null hypothesis H0.
(5)
Do the data provide sufficient evidence that the price of Ford stock respond to general
market conditions
(6)
Is there any evidence of multicollinearity?
Date
Ford stock Price y
Japanese Yen x1
Deutsche Mark x2
S&P500 x3
1992.1
38.3
133.2
1.64
407.36
1992.2
45.2
125.5
1.53
408.21
1992.3
39.4
119.2
1.41
418.48
1992.4
42
124.7
1.61
435.64
1993.1
52.3
121
1.61
450.16
1993.2
55.3
110.1
1.69
447.29
1993.3
64.7
105.2
1.62
459.24
1993.4
58.1
111.3
1.73
465.34
1994.1
59
103.4
1.76
463.21
1994.2
27.6
99
1.6
454.83
1994.3
27.5
98.5
1.55
466.96
1994.4
26.3
99.6
1.38
455.19
1995.1
29.5
89.4
1.39
493.15
1995.2
31.2
84.6
1.42
539.23
1995.3
28.7
98.2
1.43
578.32
1995.4
28.9
102.4
1.48
614.57
1996.1
34.8
106.3
1.52
647.05
1996.2
36.2
109.8
1.58
668.53
1996.3
32.1
110.5
1.61
672.92
1996.4
31.9
112.6
1.67
689.32
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