BASEBALL. Consider a multiple-regression model for predictingthe total number of runs scored by a Major League Baseball(MLB) team during a season. Using data on number of walks(x₁), singles (x2), doubles (x3), triples (x4), home runs (x5),stolen bases (x6), times caught stealing (x7), strike outs (x8),and ground outs (9) for each of the 30 teams during the 2019MLB season, a 1st-order model for total number of runs scored(y) was fit. The results are shown in the Minitab printout (nextcolumn).a. Write the least squares prediction equation fory = total number of runs scored by a team during the2019 season.b. Give practical interpretations of the beta estimates.c. Conduct a test of Ho: B7 0 against Ha: B7 < 0 ata = .05. Interpret the results.d. Locate a 95% confidence interval for 85 on the printout.Interpret the interval.e. Predict the number of runs scored in 2019 by yourfavorite MLB team. How close is the predicted value tothe actual number of runs scored by your team? Regression EquationRUNS = -295 + 0.122 WALKS + 0.443 SINGLES + 0.793 DOUBLES + 0.400 TRIPLES + 1.742 HOMERUNS+ 0.647 STOLEBASES - 0.754 CAUGHTSTEAL - 0.0542 STRIKEOUTS+ 0.0353 GRNDOUTSCoefficientsTermConstantWALKSSINGLESDOUBLESTRIPLESCoef SE Coef95% CI(-751, 161)-2952190.145 (-0.181, 0.425)0.1220.4430.131 (0.170, 0.716)0.7930.216 (0.343, 1.244)0.400 0.731 (-1.126, 1.926)1.742 0.237 (1.248, 2.236)0.286 (0.051, 1.243)0.733 (-2.283, 0.775)-0.0542 0.0604 (-0.1802, 0.0718)0.0353 0.0864 (-0.1449, 0.2155)HOMERUNSSTOLEBASES0.647CAUGHTSTEAL -0.754STRIKEOUTSGRNDOUTSModel SummaryS R-sq R-sq(adj)23.4900 95.30% 93.19%Analysis of VarianceSourceRegressionErrorTotalT-Value P-Value VIF-1.350.1920.840.411 5.703.380.003 2.433.670.002 1.840.550.591 1.497.360.0005.122.260.035 2.90-1.030.316 1.84-0.900.381 2.280.410.687 2.87DF Adj SS Adj MS F-Value P-Value9 223976 24886.245.100.0002011036551.829 235011

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Two measures of a baseball player's effectiveness as a hitter are the number of hits he makes in a season and thenumber of times he "bats in" a run (knows as "Runs Batted In" or RBIs). Can we predict a batter's RBIs from hisMajor League Baseball batters in 2017.hits? Below is numerical and graphical output from a computer regression of RBIs on Hits for 12 randomly selected Major League Baseball batters in 2017. Assume that the conditions for inference have been satisfied.(a) Do these data provide convincing evidence that there is a linear relationship between RBIs and Flits for MajorLeague Baseball batters in 2017? (b) Construct a 95% confidence interval for the slope of the population regression line for predicting RBIs from Hits.
o pis pe Suppose a doctor measures the height, x, and head circumference, y. of 11 children and obtains the data below. The correlation coefficient is 0.899 and the least squares regression line is y = 0.185x+ 12.276. Complete parts (a) and (b) below. Height, x Head Circumference, y 17.4 17.1 17.2 16.9 17.4 17.1 17.1 17.3 17.3 17.3 17.4 27.75 25.75 26.75 25.75 28 26.5 25.75 26.75 27 27.25 27.25 (a) Compute the coefficient of determination, R?. R2 = % (Round to one decimal place as needed) (b) Interpret the coefficient of determination k Approximately % of the variation in (Round to one decimal place as needed.) is explained by the least-squares regression model. Enter your answer in each of the answer boxes. Save for Later DUE RTTT:DY PIVT Score: o:5SYO Tor Tv attempts 3:35 PA- a 2/22/202 Type here to search insert prt sc 4+ backsp %23 6. 8.
In baseball, two statistics, the ERA (Earned Run Average) and the WHIP (Walks and Hits per Inning Pitched), are used to measure the quality of pitchers. For both measures, smaller values indicate higher quality. The following computer output gives the results from predicting ERA by using WHIP in a least-squares regression for the 2017 baseball season. Variable DF Estimate SE T Intercept 1 -5.0 0.26 - 19.3 WHIP 1 6.8 0.14 47.4 Which of the following statements is the best interpretation of the value 6.8 shown in the output? ERA is predicted to increase by 6.8 units for each 1 unit increase of WHIP. WHIP is predicted to increase by 6.8 units for each 1 unit increase of ERA. For a pitcher with 0 units of WHIP, the ERA is predicted to be approximately 6.8 units. For a pitcher with 0 units of ERA, the WHIP is predicted to be approximately 6.8 units. Approximately 6.8% of the variability in ERA is due to its linear relationship with WHIP.
What does the correlation matrix for a multiple regression analysis contain?A. Multiple correlation coefficientsB. Simple correlation coefficientsC. Multiple coefficients of determinationD. Multiple standard errors of estimate
A researcher wants to make an equation that will predict a person's support for domestic surveillance from a variety of demographic characteristics (e.g., age, income). What method will they use? A) Multiple regression B) Correlation C) Two-factor ANOVA D) One-sample t-test
Data from 10 Western European countries: summary statistics show that the mean percent of teens that use marijuana is 23.9 with a standard deviation of 15.6. The mean percent of teens that use other drugs is 11.6 with a standard deviation of 10.2. The correlation coefficient is r= 0.93 Find the equation of the least squares regression line considering Marijuana Use as the Explanatory variable and Other Drug Use as the Response variable. O a. ý = 7.43 + 1.42x O b. ý = - 1.42 -0.61x %3D Oc = -2.98 +0.61x %3D O d. ý = 6.10 +2.98x
28
A researcher records data on 7 adult pairs' heights (in inches) to compare the physical characteristics of brothers and sisters. Brother Sister 71 69 68 64 6 65 67 63 70 65 71 62 66 62 Mean 68.4285 64.2857 SD 2.2253 2.4299 r=0.4050 What would the least-squares regression equation be for predicting the brother's height from the sister's? A. brother's height = 0.037+44.58 * sister's height B. brother's height = 44.58 + 0.371* sister's height C. brother's height = 20.71 + 0.029 * sister's height D. brother's height = 3.28- 40.68 * sister's height If the sister's height is the same as the mean (64.2857 inches), what would the brother's predicted height be A. 68.4285 (the same as the mean as well) B. 62.1234 C. 70.8990 D. None of the above. Which of the following would be correct? A. The pair of means, (68.4285, 64.2857), lies on the linear regression line. B. The effectiveness of the linear regression model is about 16%, C. The effectiveness of the linear regression model is 10096. D. Both…
11. For temperature (x) and number of ice cream cones sold per hour (y). (65, 8), (70, 10), (75, 11), (80,13), (85, 12), (90, 16). Interpret the coefficient of determination. Optional Answers: 1. 88.2% of the variability in the number of cones sold is explained by the least-squares regression model. 2. 93.9% of the variability in the number of cones sold is explained by the least-squares regression model. 3. 88.2% of the variability in the temperature is explained by the least-squares regression model. 4. 93.9% of the variability in the temperature is explained by the least-squares regression model.

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a. Write the least squares prediction equation for y = total number of runs scored by a team during the 2019 season. b. Give practical interpretations of the beta estimates. c. Conduct a test of Ho: 37 = 0 against Ha: B7 < 0 at a = .05. Interpret the results.