Question
The stock price ( y , in $) of a certain company over a twelve-day period, the number of shares (in 100s) of company's stocks
The stock price (y, in $) of a certain company over a twelve-day period, 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 | 951 | 11.25 |
2 | 86.00 | 944 | 11.00 |
3 | 84.00 | 941 | 12.00 |
4 | 83.00 | 929 | 11.50 |
5 | 84.50 | 936 | 11.75 |
6 | 84.00 | 934 | 13.25 |
7 | 82.00 | 931 | 13.00 |
8 | 80.00 | 939 | 14.75 |
9 | 78.50 | 926 | 15.25 |
10 | 79.00 | 899 | 16.75 |
11 | 77.00 | 874 | 16.75 |
12 | 77.50 | 871 | 17.25 |
Excel was used to determine the least squares regression equation. Part of the computer output is shown below.
df | SS | MS | F | Significance F | |
---|---|---|---|---|---|
Regression | 2 | 116.1407 | 58.0704 | 33.1285 | 0.0001 |
Residual | 9 | 15.7759 | 1.7529 | ||
Total | 11 | 131.9167 |
Coefficients | Standard Error | t Stat | P-value | |
---|---|---|---|---|
Intercept | 89.0653 | 30.7151 | 2.90 | 0.0176 |
(x1) | 0.0112 | 0.0290 | 0.39 | 0.7074 |
(x2) | 1.2770 | 0.3314 | 3.85 | 0.0039 |
(a)Use the output shown above and write an equation that can be used to predict the price of the stock. (Round your numerical values to four decimal place.) =
89.0653+.0112x1.2770x2
(b)Interpret the coefficients of the estimated regression equation that you found in part (a). (Give your answers in dollars. Round your answers to four decimal places.)As the number of shares of the stock sold goes up by 100 units, the stock price goes up by $ when the volume of exchange on the NYSE is held constant. As the volume of exchange on the NYSE goes up by 1 million, the stock price goes down by $ when the number of shares of the stock sold is held constant.(c)Test whether or not there is a significant relationship between the stock price and the independent variables. Use a 0.01 level of significance.State the null and alternative hypotheses.H0: One or more of the parameters is not equal to zero. Ha: 1 = 2 = 0H0: 0 0 Ha: 0 = 0 H0: 1 = 2 = 0 Ha: One or more of the parameters is not equal to zero.H0: 1 = 2 = 0 Ha: All the parameters are not equal to zero.H0: 0 = 0 Ha: 0 0Find the value of the test statistic. (Round your answer to four decimal places.)Find the p-value. (Round your answer to four decimal places.)p-value = State your conclusion.Do not reject H0. There is insufficient evidence to conclude there is a significant relationship between the stock price and the independent variables.Reject H0. There is sufficient evidence to conclude there is a significant relationship between the stock price and the independent variables. Reject H0. There is insufficient evidence to conclude there is a significant relationship between the stock price and the independent variables.Do not reject H0. There is sufficient evidence to conclude there is a significant relationship between the stock price and the independent variables.(d)At a 0.01 level of significance, determine which variables are significant and which are not.Perform the test of significance for the number of shares (in 100s) of company's stocks sold.H0:1 = 0Ha:1 0Find the value of the test statistic. (Round your answer to two decimal places.)Find the p-value. (Round your answer to four decimal places.)p-value = What is your conclusion at the 0.01 level of significance?Do not reject H0. There is insufficient evidence to conclude that the number of shares (in 100s) of company's stocks sold is a significant factor.Do not reject H0. There is sufficient evidence to conclude that the number of shares (in 100s) of company's stocks sold is a significant factor. Reject H0. There is insufficient evidence to conclude that the number of shares (in 100s) of company's stocks sold is a significant factor.Reject H0. There is sufficient evidence to conclude that the number of shares (in 100s) of company's stocks sold is a significant factor.(e)If on a given day, the number of shares of the company that were sold was 94,800 and the volume of exchange on the New York Stock Exchange was 19 million, what would you expect the price (in $) of the stock to be? (Round your answer to two decimal places.)$
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