1. Which of the following is NOT a true statement about a regression ANOVA: Sele
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Question
1. Which of the following is NOT a true statement about a regression ANOVA:
Select one:
a. It is a test of the null hypothesis, Beta = 0, where Beta is the slope of the population regression line
b. It is a test of how much better we can improve our estimate of the quantitative dependent variable y, when we have information about a quantitative independent variable x, compared to using of the mean of y as our estimate of y.
c. The statistical hypothesis test that is performed in a regression ANOVA is unrelated to the statistical test performed when we test the population correlation coefficient, i.e., the results of one test tells us nothing about the results of the other test.
3. Which of the following is NOT a true statement about an ANOVA where the independent variable is categorical:
Select one:
a. It is a test of the null hypothesis that the population means of all groups are equal.
b. It is a test of how much better we can improve our estimate of the quantitative dependent variable y, when we have information about a categorical independent variable x, compared to using of the mean of y as our estimate of y.
c. When there are only two groups, an ANOVA is unrelated to a t-test.
d. When there are only two groups, the Mean Square Error in the ANOVA is exactly equal to the pooled sample variance calculated in a t-test assuming equal variances.
3. Which of the following statements is true:
Select one:
a. In hypothesis tests about population means, we use a z-test when we know the population variances, and a t-test when the population variances are unknown
b. When comparing the means of two populations, when variances are unknown, we use an ANOVA to test for the equality of variances.
c. When population variances are unknown, we should construct a pooled sample variance, regardless of whether the population variances are equal or not, because this will improve our estimates of the population variance.
d. The Satterthwaite correction should never be used, because it is complicated, and difficult to calculate.
e. The pooled estimate of population variance is calculated by taking the average between sample variances of both samples, i.e., by adding the sample variances and dividing by 2.
4. The slope of a regression line measures:
Select one:
a. The strength of association between two quantitative random variables
b. The change in the quantitative dependent variable given a unit change in the quantitative independent variable
c. The proportion of variation accounted for by the regression
d. All of the above
Explanation / Answer
Question 1: Option (C)
c. The statistical hypothesis test that is performed in a regression ANOVA is unrelated to the statistical test performed when we test the population correlation coefficient, i.e., the results of one test tells us nothing about the results of the other test.
Question 2: Option (B)
It is a test of how much better we can improve our estimate of the quantitative dependent variable y, when we have information about a categorical independent variable x, compared to using of the mean of y as our estimate of y.
Question 3: Option (A)
a. In hypothesis tests about population means, we use a z-test when we know the population variances, and a t-test when the population variances are unknown
Question 4: option (D)
all of the above
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