Using the accompanying Home Market Value data, develop a multiple linear regression model for estimating the market value as a function of both the age and size of the house. State the model and explain R, Significance F, and p-values, with an alpha of 0.05. E Click the icon to view the Home Market Value data.
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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?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.A group of students measure the length and width of a random sample of beans. They are interested in investigating the relationship between the length and width. Their summary statistics are displayed in the table below. All units, if applicable, are millimeters. Mean width: 7.555 Stdev width: 0.914 Mean height: 12.686 Stdev height: 1.634 Correlation coefficient: 0.8203 d) If the students are interested in using the height of the beans to predict the width, calculate the slope of this new regression equation. e) Write the equation of the best-fit line that can be used to predict bean widths. Use x to represent height and y to represent width.
- (a) The standard error Se of the linear regression model is given in the printout as "S." What is the value of Se?Use the given data to find the scatterplot, equation of the regression line, and prediction. x 1.2 1.4 1.6 1.8 2.0 y 54 53 55 54 56 Let α=0.05 Scatterplot from the calculator: What is the linear regression equation? (Round to 3 decimal places) ^ y= _________________________________________________________________ r = _______________ critical value from table: ________________ Is there a strong enough linear correlation to use the regression equation given? ___________ Explain why? _____________________________________________________ What is the best predicted y-value when x=1.9 ? _______________The U.S. Postal Service is attempting to reduce the number of complaints made by the public against its workers. To facilitate this task, a staff analyst for the service regresses the number of complaints lodged against an employee last year on the hourly wage of the employee for the year. The analyst ran a simple linear regression in SPSS. The results are shown below. Table 7: Model Summary Model R R Square Adjusted R Square Std. Error of the Estimate 1 .854a .730 .695 6.6235 a. Predictors: (Constant), Hourly Wage Table 8: ANOVA ANOVAb Model Sum of Squares df Mean Square F Sig. 1 Regression 1918.458 1 1918.458 129.783 .000a Residual 709.567 48 14.782 Total 2628.025 49 a. Predictors: (Constant), Hourly Wage b. Dependent Variable: Number of Complaints Table 9: Coefficients Coefficientsa Model Unstandardized Coefficients Standardized Coefficients t…
- The U.S. Postal Service is attempting to reduce the number of complaints made by the public against its workers. To facilitate this task, a staff analyst for the service regresses the number of complaints lodged against an employee last year on the hourly wage of the employee for the year. The analyst ran a simple linear regression in SPSS. The results are shown below. Table 7: Model Summary Model R R Square Adjusted R Square Std. Error of the Estimate 1 .854a .730 .695 6.6235 a. Predictors: (Constant), Hourly Wage Table 8: ANOVA ANOVAb Model Sum of Squares df Mean Square F Sig. 1 Regression 1918.458 1 1918.458 129.783 .000a Residual 709.567 48 14.782 Total 2628.025 49 a. Predictors: (Constant), Hourly Wage b. Dependent Variable: Number of Complaints Table 9: Coefficients Coefficientsa Model Unstandardized Coefficients Standardized Coefficients t…A marketing manager conducted a study to determine the relationship between money spent on advertising (X) and company sales (Y). The study consisted of 8 companies and the data is given below and is in units of $1000s (ie. 2.4 = $2400.00) d. What is the resulting residual value when advertising expenditure is $2200.00 (X = 2.2), that is the difference between the actual observed value of y and the predicted value of y when using the fitted regression equation? e. What percentage of the variation in company sales is explained by the regression equation? In other words, what is the variability in Y that is due to advertising? Does a…Working as a professor, I may want to try and predict success on a final exam by student success on exam 1 and see whether or not there is a relationship between those. I gather data from a set of students and obtain their first exam score and their final exam score. Using the following data, find the Pearson’s r correlation coefficient, produce a linear regression equation, and describe the associated R2 value. First exam score (X) Final exam score (Y) 95 100 90 92 95 90 85 90 85 85 80 75 65 75 60 50 70 82 90 95 80 100 90 90 75 60 75 80 Pearson’s r = ______________ Is the r significant? _______________ Linear regression equation: ____________________
- The Tiliche Corp. analyst conducted 10 independent timing studies in the manual spray painting section of the finishing department. The product line under study revealed a direct relationship between spray painting time and product surface area. The following data were collected (ignore the rating factor): (image) To answer:(a) Find the linear model relating standard time (y) to surface area (x) using linear regression. b) How much time would you assign to spray painting a new part with a surface area of 250 in2? c) Obtain the fitted value of y and the corresponding residual for a particular assembly (study #3) with a surface area of 150 square inches. d) Perform a significance test of the regression using α= 0.05. Find the P-value for this test. What are your conclusions? e) Estimate the standard errors of the slope and the value of the intercept. f) Calculate the coefficient of determination R2 . g) Calculate the correlation coefficient r. Note: The exercise in the image is…The Tiliche Corp. analyst conducted 10 independent timing studies in the manual spray painting section of the finishing department. The product line under study revealed a direct relationship between spray painting time and product surface area. The following data were collected (ignore the rating factor): (image) To answer:(a) Find the linear model relating standard time (y) to surface area (x) using linear regression. b) How much time would you assign to spray painting a new part with a surface area of 250 in2? c) Obtain the fitted value of y and the corresponding residual for a particular assembly (study #3) with a surface area of 150 square inches. Note: The exercise in the image is the original, it is in Spanish, but it is easy to understand.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