Answer true or false to the following statements and explain your answers. a. If the F-test for the utility of a multiple linear regression rejects the null hypothesis, then all the population regression coefficients are different from 0. b. If the F-test for the utility of a multiple linear regression does not reject the null hypothesis, we can conclude that there is no relationship whatsoever between the response variable and the predictor variables. c. If the value of the F-statistic for testing the utility of the multiple linear regression is close to 0, the value of the coefficient of multiple determination will be close to 0.

Answer true or false to the following statements and explain your answers. a. If the F-test for the utility of a multiple linear regression rejects the null hypothesis, then all the population regression coefficients are different from 0. b. If the F-test for the utility of a multiple linear regression does not reject the null hypothesis, we can conclude that there is no relationship whatsoever between the response variable and the predictor variables. c. If the value of the F-statistic for testing the utility of the multiple linear regression is close to 0, the value of the coefficient of multiple determination will be close to 0.

College Algebra

7th Edition

ISBN:9781305115545

Author:James Stewart, Lothar Redlin, Saleem Watson

Publisher:James Stewart, Lothar Redlin, Saleem Watson

Chapter1: Equations And Graphs

Section: Chapter Questions

Problem 10T: Olympic Pole Vault The graph in Figure 7 indicates that in recent years the winning Olympic men’s...

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Olympic Pole Vault The graph in Figure 7 indicates that in recent years the winning Olympic men’s pole vault height has fallen below the value predicted by the regression line in Example 2. This might have occurred because when the pole vault was a new event there was much room for improvement in vaulters’ performances, whereas now even the best training can produce only incremental advances. Let’s see whether concentrating on more recent results gives a better predictor of future records. (a) Use the data in Table 2 (page 176) to complete the table of winning pole vault heights shown in the margin. (Note that we are using x=0 to correspond to the year 1972, where this restricted data set begins.) (b) Find the regression line for the data in part ‚(a). (c) Plot the data and the regression line on the same axes. Does the regression line seem to provide a good model for the data? (d) What does the regression line predict as the winning pole vault height for the 2012 Olympics? Compare this predicted value to the actual 2012 winning height of 5.97 m, as described on page 177. Has this new regression line provided a better prediction than the line in Example 2?
For each of the following, explain what is wrong and why. a)In simple linear regression, the null hypothesis of the ANOVA F test is H0: β0 = 0. b)In an ANOVA table, the mean squares add. In other words, MST = MSM + MSE. c)The smaller the P-value for the ANOVA F test, the greater the explanatory power of the model. d)The total degrees of freedom in an ANOVA table are equal to the number of observations n.
Answer true or false to each of the following statements and explain your answers.a. Statistical methods designed for a particular set of assumptions may not perform well if the assumptions are violated.b. The presence of outliers in the values of the response variable can result in decreased values of the t-statistics for the utility of individual predictor variables.c. Generally, a regression model will predict as well or better for a new set of data than for the data from which it was developed.
A researcher recorded the number of e-mails received in a month and the number of online purchases made during that month for 50 people with an online presence. The resulting data were used to conduct a hypothesis test to investigate whether the slope of the population regression line relating number of e-mails received to number of online purchases is positive. What are the correct hypotheses for the test? H0:β1=0Ha:β1≠0H0:β1=0Ha:β1≠0 A H0:β1=0Ha:β1>0H0:β1=0Ha:β1>0 B H0:β1=0Ha:β1<0H0:β1=0Ha:β1<0 C H0:β1>0Ha:β1=0H0:β1>0Ha:β1=0 D H0:b1=0Ha:b1≠0 E
Suppose that you perform a hypothesis test for the slope of the population regression line with the null hypothesis H0: ß1 = 0 and the alternative hypothesis Ha: ß1 ? 0. If you reject the null hypothesis, what can you say about the utility of the regression equation for making predictions?
Answer true or false to each of the following statements and explain your answers. a. Multicollinearity occurs when two or more of the predictor variables are highly intercorrelated. b. The variance inflation factor, VIF, for a predictor variable cannot change as we add other predictor variables to the regression equation. c. If the points in a three-dimensional scatterplot of predictor variables x1, x2, and x3 lie approximately on a line or a plane, the VIF s for these predictor variables will be close to zero.
Which of the following is not one of the statistical assumptions behind linear regression? a. The residuals should not be autocorrelated. b. The variance of Y for all combinations of X variable values should be constant. c. The X variables should be normally distributed. d. The residuals should be normally distributed.
Answer true or false to each of the following statements and explain your answers.a. In using the forward selection method, a predictor variable entered into the regression equation cannot be removed at a later step.b. In the backward elimination method, only one regression analysis needs to be obtained at each step.c. If a regression equation is determined by the forward selection method, the absolute value of the t-statistic for the utility of each predictor variable in the final regression equation must be greater than tenter.
You initially said that the most appropriate statistical analysis for the data is a one sample means t test. Would a one sample t test be more appropriate than a regression?
If a new independent variable is added to a regression equation, the adjusted R2 increases only if the absolute value of the t-statistic of the new variable is greater than one. Group of answer choices True False.
Suppose that R2 = 1 for a data set. What can you say abouta. SSE?b. SSR?c. the utility of the sample multiple linear regression equation for making predictions?
6) The following results are from data where the dependent variable is EXPENSE FEES, the independent variables are SAFETY RATING, PERFORMANCE, and LOAD which is a dummy variable = 1 for load funds and = 0 for no-load funds. d) What is the standard error of the error term in the regression equation? e) Are any of the explanatory (independent) variables significant at the 10% level of significance? How do you know? f) What is the null and alternative hypothesis that Excel is testing in reporting the t-stats above?