1. Indicate whether the following statements are true or false and explain: a) i
ID: 3155188 • Letter: 1
Question
1. Indicate whether the following statements are true or false and explain:
a) if the hypothesis H: 1 = 0 is rejected, then it can be safely concluded that x causes y?
b) Suppose a regression of y on x is run and the t statistics for the testing H: 1 = 0 versus H: 1 0 has a p value of 0.0295 associated with it. Using a 5% level of significance, the null hypothesis should be rejected.
c) If the correlation between y and x is 0.9, then the r² value for a regression of y of x is 90%.
d) long as the r² value is high for an estimated regression, it is safe to use the equation to predict for any value of x.
e) If the r² value for a regression of y on x is 75%, then the r² value for a regression of x on y is also 75%.
2. Suppose a regression analysis provides the following results:
b 1, b1= 2, S= 0.05, S 0.25, SST = 117.2873, SSE = 30.0 and n = 24
Use this information to solve the following problems.
a) Test the hypothesis
H: 1 = 0
H: 1 0
Using a 5% level of significance. State the decision rule, the test statistics, and your decision. Use a t test
b) Compute the r² for the regression.
3. Suppose a regression analysis provides the following results:
b 4.0, b1= 10.0, Sb = 1.0, S = 4.0, SS = 67.36, SSE = 50.0, and n = 20.
Use this information to solve the following problems.
a) Test the hypothesis
H: 1 = 0
H: 1 0
Using a 5% level of significance. State the decision rule, the test statistics, and your decision. Use a test. Compute the r² for the regression.
b) Test the hypothesis
H: 1 0
H: 1 > 0
Using a 5% level of significance. State the decision rule, the test statistics, and your decision. Use a t test.
c) Compute the r² for the regression.
Explanation / Answer
c) If the correlation between y and x is 0.9, then the r² value for a regression of y of x is 90%. FALSE.
The value of r^2 is 0.9*0.9=0.81
d) long as the r² value is high for an estimated regression, it is safe to use the equation to predict for any value of x. True.
As the value of r2 increases, one can place more confidence in the predictive value of the regression line.
b) Suppose a regression of y on x is run and the t statistics for the testing H: 1 = 0 versus H: 1 0 has a p value of 0.0295 associated with it. Using a 5% level of significance, the null hypothesis should be rejected. True.
Since the P is low the null must go.
e) If the r² value for a regression of y on x is 75%, then the r² value for a regression of x on y is also 75%. FALSE.
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