Concept explainers
(a)
Whether the statement is correct or not and the reason for the same.
(a)
Answer to Problem 9E
Solution: The provided situation is incorrect because the hypothesis is tested using the slope coefficients of the regression equation. Hence, it should be:
Explanation of Solution
The provided situation is incorrect because the test statistic for the null hypothesis has been incorrectly recorded. The null and alternative hypotheses in the regression equation check the significance of the explanatory variables by equating their slope coefficients to zero versus not, or less than or more than zero. Hence, the null hypothesis should be written as
(b)
Whether the statement is correct or not and the reason for the same.
(b)
Answer to Problem 9E
Solution: The provided situation is incorrect because the
Explanation of Solution
The provided statement is incorrect. This is because
(c)
Whether the statement is correct or not and the reason for the same.
(c)
Answer to Problem 9E
Solution: The provided situation is incorrect because the meaning of p-value being too small is that it will be less than the significance level. Hence, the null hypothesis will be rejected implying that at least one of the explanatory variables differs from zero.
Explanation of Solution
The provided statement is incorrect. The p-value in ANOVA F-test does not mean that all the explanatory variables are significantly different from 0. This is because the null hypothesis in ANOVA states that one or more than one independent variables are equal to zero versus the alternative hypothesis that at least one of them significantly differs from zero. Hence, if the value of p-value is too small, it means that it will be less than the significance level. Hence, the null hypothesis will be rejected implying that at least one of the explanatory variables differs from zero.
Want to see more full solutions like this?
Chapter 11 Solutions
Introduction to the Practice of Statistics: w/CrunchIt/EESEE Access Card
- The linear correlation between an independent (x) and dependent (y) variable A. Is the foundation for simple (bivariate) regression B. Does not indicate a causal relationship, though one might exist C. Can be direct, inverse, or nonexistent D. Can be used to predict the value of y for any observed value of x E. All of the above F. None of the abovearrow_forwardWhat are the assumptions of simple linear regression (and as a consequence the pearson’s r correlation)?arrow_forwardIn a partially destroyed laboratory, record of an analysis of correlation, data, the following results only are legible:Variance of X=9. Regression equation: 8X –10Y + 66=0, 40X–18Y = 214.(1) the mean value X and Y,(2) the correlation coefficient between X and Y, and (3) the standard deviation of Y ?arrow_forward
- True or False? The sample correlation coefficient is equal to the covariance of x and y divided by the square root of the product of sx2 times sy2.arrow_forwardYou have estimated a multiple regression model with 6 explanatory variables and an intercept from a sample with 46 observations. What is the critical value of the test statistic (tc) if you want to perform a test for the significance of a single right-hand side (explanatory) variable at α = 0.05? a.) 2.023 b.) 2.708 c.) 2.423 d.) 2.704arrow_forward1. Explain the purpose or use of the following:a. Linear regression equationb. Correlation coefficient.arrow_forward
- What is the purpose of multiple linear regression? a. To assess whether there is a significant difference between independent groups b. To predict scores of an independent variable from scores of a single dependent variable c. To predict scores of a single dependent variable from scores on multiple independent variables d. To predict scores of an independent variable from scores on multiple dependent variablesarrow_forwardWhich of the following best describes the difference between the interpretation of the correlation coefficient and the beta coefficient for a regression equation expressing the relationship between variables X and Y? A) The beta coefficient represents the linear relationship between X and Y, whereas the correlation coefficient represents the percent variability in Y explained by XB) The beta coefficient represents the difference between observed and expected values of Y, whereas the correlation coefficient represents the linear relationship between X and Y.C) The beta coefficient predicts increases or decreases in Y with increases or decreases in X, whereas the correlation coefficient provides a unit-free measure of the strength of the relationship.D) The correlation coefficient predicts increases or decreases in Y with increases or decreases in X, whereas the beta coefficient provides a unit-free measure of the strength of the relationship.arrow_forwardWhat is the null hypothesis when testing for significance using the Pearson correlation coefficient? a. µ1 = µ2 b. r = 0 c. ρ = 0 d. r x 0arrow_forward
- Glencoe Algebra 1, Student Edition, 9780079039897...AlgebraISBN:9780079039897Author:CarterPublisher:McGraw Hill