Answer true or false to each of the following statements and explain your answers. a. In a regression equation involving a quantitative predictor variable x1 and a single indicator variable x2, the t-test of the utility of the interaction term is a test that the regression lines are parallel for the two values of the qualitative variable. b. If the regression lines relating the response variable y to a quantitative predictor variable x1 have the same y-intercept for each category of a qualitative predictor variable, then there is no interaction between the two predictor variables.

Answer true or false to each of the following statements and explain your answers. a. In a regression equation involving a quantitative predictor variable x1 and a single indicator variable x2, the t-test of the utility of the interaction term is a test that the regression lines are parallel for the two values of the qualitative variable. b. If the regression lines relating the response variable y to a quantitative predictor variable x1 have the same y-intercept for each category of a qualitative predictor variable, then there is no interaction between the two predictor variables.

Functions and Change: A Modeling Approach to College Algebra (MindTap Course List)

6th Edition

ISBN:9781337111348

Author:Bruce Crauder, Benny Evans, Alan Noell

Publisher:Bruce Crauder, Benny Evans, Alan Noell

Chapter5: A Survey Of Other Common Functions

Section5.6: Higher-degree Polynomials And Rational Functions

Problem 1TU: The following fictitious table shows kryptonite price, in dollar per gram, t years after 2006. t=...

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The following fictitious table shows kryptonite price, in dollar per gram, t years after 2006. t= Years since 2006 0 1 2 3 4 5 6 7 8 9 10 K= Price 56 51 50 55 58 52 45 43 44 48 51 Make a quartic model of these data. Round the regression parameters to two decimal places.
Answer true or false to each of the following statements and explain your answers. a. The number of indicator variables required to represent the possible values of a qualitative predictor variable is one more than the number of possible values. b. If we take the regression equation relating the response variable y to a quantitative predictor variable x1 and indicator variables x2 and x3 to be y = β0 + β1x1 + β2x2 + β3x3, then we are assuming there is no interaction between x1 and the qualitative variable represented by x2 and x3. c. A cross-product term in a regression equation is often referred to as an interaction term.
Given the following information regarding a dependent variable (Y) and an independent variable (X) Y X 6 2 8 1 4 4 2 3 1 5 A. Develop the least squared error estimated regression equation.B. Calculator r ^ 2, the coefficient of determination, and r, the coefficient of correlation.
Answer true or false to the following statements and explain your answers. a. In a multiple linear regression analysis, the test of H0: β1 = 0 can be affected by what other predictor variables are in the multiple linear regression equation. b. If the F-test for the utility of the multiple linear regression equation rejects the null hypothesis of H0: β1 = β2 = ... = βk = 0, then each individual t-test of H0: βi = 0, i = 1,... , k, will result in rejection of the null hypothesis. c. The number of degrees of freedom for the tα/2-value used in constructing a confidence interval for a population regression coefficient is the same as the number of degrees of freedom for the mean square error (MSE).
Answer true or false to the following statements and explain your answers.a. In a multiple linear regression analysis, the test of H0: ß1 = 0 can be affected by what other predictor variables are in the multiple linear regression equation.b. If the F-test for the utility of the multiple linear regression equation rejects the null hypothesis of H0: ß1 = ß2 = ... = ßk = 0, then each individual t-test of H0: ßi = 0, i = 1,... , k, will result in rejection of the null hypothesis.c. The number of degrees of freedom for the ta/2-value used in constructing a confidence interval for a population regression coefficient is the same as the number of degrees of freedom for the mean square error (MSE).
28. Below is some of the regression output from a regression of the amount rental houses on an island rent for (expressed in thousands of $'s) based on the size of the house (expressed in square feet), whether the house has an ocean front view (VIEW = 1 if it has an ocean front view and = 0 if not), and an interaction term between the ocean front view dummy variable and the size of the house. If the estimated equation is:Price = 1,251 + 0.34*Size + 1,538*View + 0.07*(Size*View) Suppose you just built a house with an ocean front view that is 3600 square feet and you want to decide how much to rent it for. What is the predicted price of a house that is 3600 square feet and has an ocean front view? (please express your answer using 1 decimal places)
29. Below is some of the regression output from a regression of the amount rental houses on an island rent for (expressed in thousands of $'s) based on the size of the house (expressed in square feet), whether the house has an ocean front view (VIEW = 1 if it has an ocean front view and = 0 if not), and an interaction term between the ocean front view dummy variable and the size of the house. If the estimated equation isPrice = 1,444 + 0.3*Size + 1,411*View + 0.08*(Size*View) How much more (or less) does a 3800 square foot house that has an ocean front view rent for compared to a similar sized house without an ocean front view? (if the ocean front house rents for more then express your answer as a POSITIVE number; if the ocean front house rents for less then express your answer as a NEGATIVE number) (please express your answer using 1 decimal places)
Given the equation of a regression line is y= -1.5x-1.8, what is the best predicted value for y given x= -3.0? Assume that the variables x and y have significant correlation.
The director of marketing at Vanguard Corporation believes that sales of the company's Bright Side laundry detergent (S) are related to Vanguard's own advertising expenditure (A), as well as the combined advertising expenditures of its three biggest rival detergent (R). The marketing director collects 36 weekly observations on S, A and R to estimate the following multiple regression equation: S = a + bA + cR .where, S, A, and R are measured in dollars per week. Vanguard's marketing director is comfortable using parameter estimates that are statistically significant at the 10% level or better.DEPENDENT VARIABLE: S R-SQUARE F-RATIO P-VALUE ON FOBSERVATIONS: 36 0.2247 4.781 0.0150VARIABLE PARAMETER STANDARD T-RATIO P-VALUE ESTIMATE ERRORINTERCEPT 175086.0 63821.0 2.74 0.0098A 0.8550 0.3250…
Question 5 - what is the y-intercept of the equation of the regression line y = 36.11695 + 7.20508x A. 7.20508 B. 36.11695 C. Y D. X Question 6 - what is the slop of the equation of the regression line y = 36.11695 + 7.20508x? A. 7.20508 B. 36.11695 C . Y D . X
Consider the following model:? = ?? + ?,known as the Classical Linear Regression Model (CLRM), where y is the dependent variable, X is the set of independent variables, ? is the vector of parameters to be estimated and ? is the error term. Present and discuss the R2 and the adjusted R2. Discuss pros and cons of each of the two statistics.
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.