Suppose X, is a numerical variable and X, is a dummy variable with two categories and the regression equation for a sample of n=23 is î, =9+5X, - 3X a. Interpret the regression coefficient associated with variable X,. b. Interpret the regression coefficient associated with variable X,. c. Suppose that the tsTAT test statistic for testing the contribution of variable X, is - 0.68. At the 0.10 level of significance, is there evidence that variable X, makes a significant contribution to the model? a. Interpret the regression coefficient associated with variable X,. Holding constant the effect of X,, for each increase of one unit in X,, the predicted mean value of Y increases by a positive change of 5 unit(s). b. Interpret the regression coefficient associated with variable X,. Holding constant the value of X,, changing the value of X, from 0 to 1 is estimated to decrease the predicted mean value of Y by a positive change of 3 unit(s). c. Determine the null and alternative hypotheses. Họ: B, = 0 H;: B * 0 State the test statistic. tSTAT = (Round to two decimal places as needed.)

Suppose X, is a numerical variable and X, is a dummy variable with two categories and the regression equation for a sample of n=23 is î, =9+5X, - 3X a. Interpret the regression coefficient associated with variable X,. b. Interpret the regression coefficient associated with variable X,. c. Suppose that the tsTAT test statistic for testing the contribution of variable X, is - 0.68. At the 0.10 level of significance, is there evidence that variable X, makes a significant contribution to the model? a. Interpret the regression coefficient associated with variable X,. Holding constant the effect of X,, for each increase of one unit in X,, the predicted mean value of Y increases by a positive change of 5 unit(s). b. Interpret the regression coefficient associated with variable X,. Holding constant the value of X,, changing the value of X, from 0 to 1 is estimated to decrease the predicted mean value of Y by a positive change of 3 unit(s). c. Determine the null and alternative hypotheses. Họ: B, = 0 H;: B * 0 State the test statistic. tSTAT = (Round to two decimal places as needed.)

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Description: Find the T Statistic Find the P ValueRound to three decimal places Suppose X, is a numerical variable and X, is a dummy variable with two categories and the regression equation for a sample of n= 23 is Y; = 9+5X, - 3X2;-a. Interpret the regression co

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?
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.
A researcher would like to predict the dependent variable YY from the two independent variables X1X1 and X2X2 for a sample of N=10N=10 subjects. Use multiple linear regression to calculate the coefficient of multiple determination and test statistics to assess the significance of the regression model and partial slopes. Use a significance level α=0.01α=0.01. X1X1 X2X2 YY 58.8 29.9 63.1 64.1 57.3 40.1 51.4 35.3 46.2 77.1 88.5 30 60.6 67.5 16.2 68.3 63.4 62 44.8 6.6 77.6 49 29.3 65.5 55.5 25.8 62.5 57.5 30.2 62 R2=R2= F=F= P-value for overall model = t1=t1= for b1b1, P-value = t2=t2= for b2b2, P-value = What is your conclusion for the overall regression model (also called the omnibus test)? The overall regression model is statistically significant at α=0.01α=0.01. The overall regression model is not statistically significant at α=0.01α=0.01. Which of the regression coefficients are statistically different from zero? neither regression coefficient is…
A researcher would like to predict the dependent variable YY from the two independent variables X1X1 and X2X2for a sample of N=20N=20 subjects. Use multiple linear regression to calculate the coefficient of multiple determination and test the significance of the overall regression model. Use a significance level α=0.02. X1X1 X2X2 YY 31.4 32.3 25.2 85.4 28.1 53 66.3 42.6 67.4 59 56.1 70.7 52.4 40.4 39.7 86.4 23.7 35 50.9 36.7 34.4 74.4 38 64.9 57.3 47.6 67.4 61.9 33.3 41.3 48.6 49.7 53.6 46.6 47.2 34.5 31.8 38.7 40.9 86 55 74 69.8 27.7 45.9 65.8 48.2 42.4 44.7 55.3 55.1 57.3 27 31.5 60.4 28.1 19.4 65.9 26 13.7 SSreg= SSres= R2= F= P-value = What is your decision for the hypothesis test? Reject the null hypothesis, H0:β1=β2=0 Fail to reject H0H0 What is your final conclusion? The evidence supports the claim that one or more of the regression coefficients is non-zero The evidence supports the claim that all of the regression…
A researcher would like to predict the dependent variable YY from the two independent variables X1X1 and X2X2 for a sample of N=11N=11 subjects. Use multiple linear regression to calculate the coefficient of multiple determination and test statistics to assess the significance of the regression model and partial slopes. Use a significance level α=0.05α=0.05. X1X1 X2X2 YY 52.3 45.6 49.1 55.9 48.7 53.1 46.5 47.4 45.9 52 45.6 59.8 48.9 45.5 52.6 46.2 35.1 71.2 28.8 32.6 33.5 40.7 41 40.3 43.7 40 65.8 47 37.8 52.8 34.2 28 53.5 R2=R2= (Not the adjusted R2R2) FF test statistic = P-value for overall model = test statistic for b1b1 p-value for the two-tailed test = test statistic for b2b2 p-value for the two-tailed test = What is your conclusion for the overall regression model at the 0.05 alpha level (also called the omnibus test)? The overall regression model is statistically significant at α=0.05α=0.05. The overall…
The following table gives the marks obtained by 10 students in POLI 344 (X) together with the marks obtained in the exam in POLI 308 (Y). POLI 344 (X)8 8 9 10 10 11 12 13 13 11 14 POLI 443 (Y) 7 11 8 7 12 11 10 12 14 17 15 (i) State the two equation lines of the regression line. (ii) If a student was absent from POLI 443 but scored 18 in POLI 344 (X) state the regression line, which would be suitable for estimating his/her possible mark in POLI 443 and work out a fair estimate for his /her possible mark.
A researcher would like to predict the dependent variable YY from the two independent variables X1X1 and X2X2for a sample of N=13N=13 subjects. Use multiple linear regression to calculate the coefficient of multiple determination and test statistics to assess the significance of the regression model and partial slopes. Use a significance level α=0.02α=0.02. X1X1 X2X2 YY 40.6 66.7 59 27.2 72.4 42.3 65 56.2 69.1 17.3 71.2 25.4 30 65.6 40.9 41.2 59.1 44.8 68.5 44.3 40.6 79.5 37.3 54.7 55.6 58 66.3 59.4 46.1 27.2 62.9 42.4 30.9 67.2 44.5 39.5 22.6 64.3 18.4 R2= F= P-value for overall model = t1= for b1, P-value = t2= for b2, P-value = What is your conclusion for the overall regression model (also called the omnibus test)? The overall regression model is statistically significant at α=0.02. The overall regression model is not statistically significant at α=0.02. Which of the regression coefficients are statistically different from zero? neither…
Given the estimated least square regression line y=2.48+1.63x, and the coefficient of determination of 0.81, What is the value of correlation coefficient?
If the standard error of the estimate for a regression model fitted to a large number of paired observations is 1.75, approximately 95% of the residuals would lie within ______. −3.50 and +3.50 −1.75 and +1.75 −0.95 and +0.95 −0.68 and +0.68 −0.97 and +0.97
Consider the multiple regression model shown next between the dependent variable Y and four independent variables X1, X2, X3, and X4, which results in the following function:Ŷ = 33 + 8X1 − 6X2 + 16X3 + 18X4For this model, there were 35 observations; SSR = 1,544 and SSE = 600. Assume a 0.01 significance level.Based on the given information, which of the following conclusions is correct about the statistical significance of the overall model? Multiple Choice Reject the null hypothesis that β3 = 0. Do not reject the null hypothesis that β1 = β2 = β3 = β4 = 0. Reject the null hypothesis that β1 = 0. Reject the null hypothesis that β1 = β2 = β3 = β4 = 0.
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.