Question 1
An academic advisor wants to predict the typical starting salary of a graduate at a top business school using the GMAT score of the school as a predictor variable. A simple linear regression of SALARY versus GMAT using 25 data points is shown below.
0 = -92040
1 = 228
s = 3213 df = 23
t = 6.67
Set up the null and alternative hypotheses for testing whether a linear relationship exists between SALARY and GMAT.
◦
H0:
β1 = 0 vs.
Ha:
β1 ≠ 0
◦
H0:
β1 = 0 vs.
Ha:
β1 > 0
◦
H0:
β1 > 0 vs. H
a: β
1 < 0
◦
H0:
1 = 228 vs.
Ha:
1 > 228
Question 2
Consider the following model
y =
β0 +
β1x +
∈, where y is the daily rate of return of a stock, and
x is the daily rate of return of the stock market as a whole, measured by the daily rate of return of Standard & Poor's (S&P) 500 Composite Index. Using a random sample of
n = 12 days from 2007, the least squares lines shown in the table below were obtained for four firms. The estimated standard error of
1 is shown to the right of each least squares prediction equation.
| Firm | Estimated Market Model | Estimated Standard Error of β1 |
| Company A | y = .0010 + 1.40x | | .03 | |
| Company B | y = .0005 - 1.21x | | .06 |
| Company C | y = .0010 + 1.62x | 1 | .34 |
| Company D | y = .0013 + .76x | | .15 |
Calculate the test statistic for determining whether the market model is useful for predicting daily rate of return of Company A's stock.
◦ 46.7
◦ 1.40
◦ 161.6
◦ 1.40 ± .067
Daily changes in photosynthesis and nitrogen fixation gene expression in Synechococcus cultures isol
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