Advanced Engineering Mathematics
10th Edition
ISBN: 9780470458365
Author: Erwin Kreyszig
Publisher: Wiley, John & Sons, Incorporated
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- The equation of the least-squares regression line is ý = 68.5 + 11.4x, where ý is the number of students enrolled and x is number of years the school has been The number of students enrolled at a school varies from year to year. For the first eight years the school is open, the number of students enrolled is recorded in the table shown. open. Which shows the residual plot? Students 92 Year 2. 94 100 104 80 4 60 113 131 40 7. 8. 147 176 20 -20 0. 2. 4. 8. Number of Years 3. 56arrow_forwardThe results shown to the right provide the X-values, residuals, and a residual plot from a regression analysis. Is there any evidence of a pattern in the residuals? Explain. Choose the correct answer below. A. Yes, the residuals show a distinct cyclical pattern. O B. Yes, the residuals show a distinct curved pattern. C. No, the residuals appear to be randomly spread. OR Yes the residuals show decreasing variation O C X 1 234567890 10 Residuals 0.78 -0.71 1.17 -0.63 2.45 -0.77 0.27 1.64 - 1.24 1.66 Residuals 3- 2- 1- ● хол- To 10arrow_forwardListed below is the multiple regression equation for predicting Y by X₁ through Xs. Y is the number of sales per month. X₁ is the number of sales calls made X2 is the number of hours on the showroom floor X3 is the amount spent on radio ads X is the number of text messages sent Xs is the number of email messages sent Regression Statistics R Square 0.634 Standard Error 7.6796 Observations 45 Intercept X₁ X₂ X3 XA Xs Coefficients Standard Error 6.8163 0.1005 -0.3207 0.2084 0.1221 0.0943 77.1211 1.9439 -11.123 0.1144 11.34 1.23 What is the computed value of the F statistic you would use to test the significance of the entire model? Round your answer to two decimal places.arrow_forward
- The percentage of the variation in the value of y this is explained by the lease squares regression line is Group of answer choices ρ the slope of the regression line. the correlation coefficient. the coefficient of determination. the y-intercept of the regression line. The data below shows the summary statistics for a regression analysis on car weight (in metric tons) and fuel consumption (in miles per gallon). b0=48.8b0=48.8 b1=−8.37b1=−8.37 r2=0.36r2=0.36 (Note that 0.362=0.13 and 0.36−−−−√=0.6)(Note that 0.362=0.13 and 0.36=0.6) Choose the correct interpretation of the y-intercept of the line:arrow_forwardA simple regression model for 10 pair of data resulted in a standard error of 3.95 (i.e., Se = 3.95), and the. The sum of squares of error (SSE) is ______. a. 187.23 b. 171.63 c. 156.03 d. 140.42 e. 124.82arrow_forwardAnnual high temperatures in a certain location have been tracked for several years. Let X represent the year and Y the-high temperature. Based on the data shown below, calculate the regression line (each value to two decimal places). y D 2. 19.44 3. 19.8 4 16.96 16.42 6. 14.78 7 14.94 8. 12.5arrow_forward
- Annual high temperatures in a certain location have been tracked for several years. Let X represent the year and Y the high temperature. Assume that temperature is independent each year. Based on the data shown below, calculate the regression line (each value to two decimal places). First the slope and then the y-intercept. Y X 3 4 5 67 8 00 a 9 y 10.14 10.85 11.86 11.17 7.58 9.79 7.5 x+arrow_forwardUse the data in the table below to complete parts (a) through (d). 39 33 40 47 42 50 59 56 51 24 22 27 32 30 31 31 27 29 Click the icon to view details on how to construct and interpret residual plots. (a) Find the equation of the regression line. (Round to three decimal places as needed.) (b) Construct a scatter plot of the data and draw the regression line. Plot the x-values on the horizontal axis and the y-values on the vertical axis. Choose the correct graph below. OA. В. Oc. OD. 34 70, (c) Construct a residual plot. Plot the x-values on the horizontal axis and the residuals on the vertical axis. Choose the correct graph below. O A. Ов. Oc. OD. (d) Determine if there are any patterns in the residual plot and explain what they suggest about the relationship between the variables. The residual plot a pattern because the residuals about 0. This implies the regression line a good representation of the relationship between the variables.arrow_forwardIn bivariate regression, the value of Y when X equals 0 is: Group of answer choices Intercept (b0) Residual Slope (b1)arrow_forward
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