Answer true or false to each of the following statements and explain your answers. a. In the forward selection method with tenter = 2.00, if the t-statistics for the three predictor variables that have not been entered are 1.72, −1.28, and 0.89, then the forward selection method stops. b. In applying the backward elimination method, a predictor variable is added to the regression equation if the absolute value of its t-statistic is greater than tremove. c. The maximum number of regression equations that need to be determined when selecting a regression equation by backward elimination is equal to the number of predictor variables.

Answer true or false to each of the following statements and explain your answers. a. In the forward selection method with tenter = 2.00, if the t-statistics for the three predictor variables that have not been entered are 1.72, −1.28, and 0.89, then the forward selection method stops. b. In applying the backward elimination method, a predictor variable is added to the regression equation if the absolute value of its t-statistic is greater than tremove. c. The maximum number of regression equations that need to be determined when selecting a regression equation by backward elimination is equal to the number of predictor variables.

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?
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.
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.
Years of Work Experience and number of Job Offers of 10 job-seekers were as follows: Work Exp. 4 2 5 3 7 12 2 5 4 9 No. of Offers 7 1 8 4 13 19 3 11 9 15 a. Fit the regression equation of No. of Job Offers on Years of Work Experience. b. What will be the predicted number of offers for an applicant with 6 years of experience? c. Verify the relationship between the number of job offers and years of work experience using at least two relevant methods
If a sample of 25 pairs of data yields a correlation coefficient, r, of 0.390 and the scatterplot displays a linear trend, can you use the regression equation to make predictions, assuming your x-values are within the domain of the data set? Choose your answer from the multiple choice answers below A.) Yes, because rcrit = 0.396 and the regression coefficient, r, is less than this value. B.) Yes, because rcrit = 0.381 and the regression coefficient, r, is greater than this value. C.) No, because rcrit = 0.381 and the regression coefficient, r, is greater than this value. D.) No, because rcrit = 0.396 and the regression coefficient, r, is less than this value.
Use the following linear regression equation to answer the questions. x1 = 1.7 + 3.9x2 – 8.5x3 + 2.2x4 Suppose x2 increased by 2 units. What would be the expected change in x1? Suppose x2 increased by 4 units. What would be the expected change in x1? (e) Suppose that n = 18 data points were used to construct the given regression equation and that the standard error for the coefficient of x2 is 0.454. Construct a 99% confidence interval for the coefficient of x2. (Use 2 decimal places.) lower limit ? upper limit ? (f) Using the information of part (e) and level of significance 10%, test the claim that the coefficient of x2 is different from zero. (Use 2 decimal places.) t ? t critical ± ?
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?
The Mayor of texas whom is partners with a local agriculturalist wants to know how the amount of fertilizer and the amount of water given to plants affect their growth. The results were inputted into MINITAB so as to fit the model a) Write out the regression equation b) What is the sample size used in this investigation? c) Determine the values of *, ** and ***, **** d) Conduct a hypothesis test, at the 5% level of significance, to determine whether ? is significant. e) What would be the growth of the plant if 4g of fertilizer and 7g of ater was given to it daily? f) Carry out an F -test at the 1% significance level to determine whether the model is significant
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.
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?
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?
(1) Write out the regression equation (2) What is the sample size used in this investigation? (3) Determine the values of *, ** and ***, ****