Refer to the following computer output from estimating the parameters of the nonlinear model Y=aRD SCT The computer output from the regression analysis is: DEPENDENT VARIABLE: OBSERVATIONS: LNY R-SQUARE 32 0.7766 F-RATIO 32.44 P-VALUE ON F 0.0001
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- A Ross MAP team is currently developing a regression model to explain the travel expense of HR consulting firms in a month (measured in thousands of dollars). So far, the team has identified the number of consultants, the number of clients, the number of air-travel trips, and the number of trips to high-expense cities (e.g., NYC, Boston, San Jose) as potential independent variables. A partial output of the corresponding regression model is in Figure 1. Use the figure to answer question 4to6 4. What is the R2 and adjusted R2 of the model? 5. What is the standard error of the estimates (serror) in thousands of dollars? 6. Based on what you can learn from this table, what is your assessment about the model? For your information, the firm with the lowest travel expense was $47K and the firm with the highest expense was $125K in the sample data.A researcher notes that, in a certain region, a disproportionate number of software millionaires were born around the year 1955. Is this a coincidence, or does birth year matter when gauging whether a software founder will besuccessful? The researcher investigated this question by analyzing the data shown in the accompanying table. Complete parts a through c below. a. Find the coefficient of determination for the simple linear regression model relating number (y) of software millionaire birthdays in a decade to total number (x) of births in the region. Interpret the result. The coefficient of determination is 1.___? (Round to three decimal places as needed.) This value indicates that 2.____ of the sample variation in the number of software millionaire birthdays is explained by the linear relationship with the total number of births in the region. (Round to one decimal place as needed.) b. Find the coefficient of determination for the simple linear regression model…Which of the multivariate regression parameters listed below would be best interpreted as: the predicted value on the dependent variable when all of the independent variables in the model are equal to zero. a b1 X1 R2
- Suppose that a multiple linear regression model was fit to data and that the following output resulted: Coefficients: (Intercept)exam1exam2attendance Estimate20.001.3002.5000.685 Std. Error4.2910.2610.2745.608 t value-4.6604.9819.124 0.122 Pr(>|t|)<0.0001<0.0001<0.00010.9032 Perform a backwards selection process. Select the variable that would be removed first from the model. The significance level is 0.05 for testing purposes. attendance exam2 exam1A multiple regression model is estimated with Excel and produces the following output: Dependant Variable: K Rs-qauare F-ratio p-value on f Observations: 23 0.5448 7.58 0.00157 Variable Parameter estimate Standard error t-ratio p-value Intercept -220.0 68.25 -3.22 0.0045 x -11.340 3.670 -3.09 0.0060 y 0.3875 0.0625 6.20 0.0001 z 4.26 2.350 1.81 0.0857 A. Write the regression equation based on the output. B. If X equals 50, Y equals 200, and Z equals 45, what value do you predict K will take? If X, Y, and Z are all equal to 0? C. At the 5 percent significance level, which one of the three estimated coefficients of X, Y and Z is (are) statistically significant? D. How much of the total variation is explained by this regression equation? E. Is the overall regression equation statistically significant at the 1 percent level of significance?The following is a partial computer output of a multiple regression analysis of a data set containing 20 sets of observations on the dependent variableThe regression equation isSALEPRIC = 1470 + 0.814 LANDVAL + 0.820 IMPROVAL + 13.5 AREA Predictor Coef SE Coef T P Constant 1470 5746 0.26 0.801 LANDVAL 0.8145 0.5122 1.59 0.131 IMPROVAL 0.8204 0.2112 3.88 0.0001 AREA 13.529 6.586 2.05 0.057 S = 79190.48 R-Sq = 89.7% R-Sq(adj) = 87.8% Analysis of Variance Source DF SS MS Regression 3 8779676741 2926558914 Residual Error 16 1003491259 62718204 Total 19 9783168000 For the problem above, we want to carry out the significance test about the coefficient of LANDVAL, what is the t-value for this test, and is it significant? 46.66, significant 2.05, significant 1.59, not significant 0.26, not significant
- The accompanying data resulted from an experiment in which weld diameter and shear strength (in pounds) were determined for five different spot welds on steel. Below are the data collected and the regression equation. Diameter Strength 200.1 813.7 210.1 785.3 220.1 960.4 230.1 1118.0 240.0 1076.2 Strength = -941.6992 + 8.5988*Diameter The predicted y-hat value for a diameter of 201 is 864. if we observed a weld that had a diameter of 235 that had a strength 1000, what would be its residual?The Update to the Task Force Report on Blood Pressure Control in Children [12] reported the observed 90th per-centile of SBP in single years of age from age 1 to 17 based on prior studies. The data for boys of average height are given in Table 11.18. Suppose we seek a more efficient way to display the data and choose linear regression to accomplish this task. age sbp 1 99 2 102 3 105 4 107 5 108 6 110 7 111 8 112 9 114 10 115 11 117 12 120 13 122 14 125 15 127 16 130 17 132 Do you think the linear regression provides a good fit to the data? Why or why not? Use residual analysis to justify your answer. Am I supposed to run a residual plot and QQ-plot for this question?Suppose that researchers obtain a random sample of adults ages 18 – 40 and collect data on the following variables: shoe size – in inches age – in years height – in inches forearm length – in inches Suppose further that a multiple linear regression model is fit to the resulting data set using R Studio and that the following output is obtained from it. Use this output to answer the question that follows: > summary(lm(shoesize ~ age + height + forearm, data = measures)) Coefficients: (Intercept)ageheightforearm Estimate10.14882 0.06045 -0.02108 -0.06479 Std. Error 4.49245 0.06838 0.06350 0.06847 t value2.259 0.884 -0.332 -0.946 Pr(>|t|) 0.0264 0.3792 0.7408 0.3467 Residual standard error: 1.719 on 85 degrees of freedomMultiple R-squared: 0.01983, Adjusted R-squared: 0.01477 F-statistic: 0.5731 on 3 and 85 DF, p-value: 0.6342 Which of the following is the correct interpretation of the Adjusted R-squared? The probability that our model…
- Suppose that researchers obtain a random sample of adults ages 18 – 40 and collect data on the following variables: shoe size – in inches age – in years height – in inches forearm length – in inches Suppose further that a multiple linear regression model is fit to the resulting data set using R Studio and that the following output is obtained from it. Use this output to answer the question that follows: > summary(lm(shoesize ~ age + height + forearm, data = measures)) Coefficients: (Intercept)ageheightforearm Estimate10.14882 0.06045 -0.02108 -0.06479 Std. Error 4.49245 0.06838 0.06350 0.06847 t value2.259 0.884 -0.332 -0.946 Pr(>|t|) 0.0264 0.3792 0.7408 0.3467 Residual standard error: 1.719 on 85 degrees of freedomMultiple R-squared: 0.01983, Adjusted R-squared: 0.01477 F-statistic: 0.5731 on 3 and 85 DF, p-value: 0.6342 What is the estimate for the standard deviation of the residuals? 1.719 0.01983 -0.946 0.6342Suppose that researchers obtain a random sample of adults ages 18 – 40 and collect data on the following variables: shoe size – in inches age – in years height – in inches forearm length – in inches Suppose further that a multiple linear regression model is fit to the resulting data set using R Studio and that the following output is obtained from it. Use this output to answer the question that follows: > summary(lm(shoesize ~ age + height + forearm, data = measures)) Coefficients: (Intercept)ageheightforearm Estimate10.14882 0.06045 -0.02108 -0.06479 Std. Error 4.49245 0.06838 0.06350 0.06847 t value2.259 0.884 -0.332 -0.946 Pr(>|t|) 0.0264 0.3792 0.7408 0.3467 Residual standard error: 1.719 on 85 degrees of freedomMultiple R-squared: 0.01983, Adjusted R-squared: -0.01477 F-statistic: 0.5731 on 3 and 85 DF, p-value: 0.6342 Which of the following is the correct conclusion for the F-test that was performed? There is strong evidence to…Suppose that researchers obtain a random sample of adults ages 18 – 40 and collect data on the following variables: shoe size – in inches age – in years height – in inches forearm length – in inches Suppose further that a multiple linear regression model is fit to the resulting data set using R Studio and that the following output is obtained from it. Use this output to answer the question that follows: > summary(lm(shoesize ~ age + height + forearm, data = measures)) Coefficients: (Intercept)ageheightforearm Estimate10.14882 0.06045 -0.02108 -0.06479 Std. Error 4.49245 0.06838 0.06350 0.06847 t value2.259 0.884 -0.332 -0.946 Pr(>|t|) 0.0264 0.3792 0.7408 0.3467 Residual standard error: 1.719 on 85 degrees of freedomMultiple R-squared: 0.01983, Adjusted R-squared: -0.01477 F-statistic: 0.5731 on 3 and 85 DF, p-value: 0.6342 What is the test-statistic is used to test whether at least one of the explanatory variables is a significant predictor of…