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.

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.

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

See similar textbooks

Similar questions

KidsFeet Regression Line y-Intercept The KidsFeet dataframe contains data collected on 39 fourth grade students in Ann Arbor, MI, in October 1997. Two of the measurements taken on the children were the length in centimeters, (length), and width in centimeters, (width), of their longest foot. This data could be used to answer the following Research Question: How is the width of a fourth-grade student's foot related to the length? Which of the following is the y-intercept of the regression line? ## ## Simple Linear Regression## ## Correlation coefficient r = 0.6411 ## ## Equation of Regression Line:## ## length = 9.817 + 1.658 * width ## ## Residual Standard Error: s = 1.025 ## R^2 (unadjusted): R^2 = 0.411 ( ) 1.0248 ( ) 1.6576 ( ) 22.8153 ( ) 0.411 ( ) 9.8172 ( )0.6411
Listed below are paired data consisting of movie budget amounts and the amounts that the movies grossed. Find the regression equation, letting the budget be the predictor (x) variable. Find the best predicted amount that a movie will gross if its budget is $110 million. Use a significance level of alpha equals 0.05 . Budget left parenthesis $ right parenthesis in Millions 42 24 119 69 77 48 121 62 5 63 129 21 12 154 4 Gross left parenthesis $ right parenthesis in Millions 117 16 112 66 111 111 104 90 62 104 219 27 20 288 42 The regression equation is ŷ = __ + __x. (Round to one decimal place as needed.) The linear coefficient of correlation r = ___ (Round to three decimal places as needed.) The critical value of r = ____ The best predicted gross for a move with a $110 million budget is _____.
The following data represents the winning percentage (the number of wins out of 162 games in a season) as well as the teams Earned Run Average, or ERA.The ERA is a pitching statistic. The lower the ERA, the less runs an opponent will score per game. Smaller ERA's reflect (i) a good pitching staff and (ii) a good team defense. You are to investigate the relationship between a team's winning percentage - Y, and its Earned Run Average (ERA) - X. Winning Proportion - Y Earned Run Average (ERA) - X 0.623457 3.13 0.512346 3.97 0.635802 3.68 0.604938 3.92 0.518519 4.00 0.580247 4.12 0.413580 4.29 0.407407 4.62 0.462963 3.89 0.450617 5.20 0.487654 4.36 0.456790 4.91 0.574047 3.75 (b) Use R-Studio to find the least squares estimate of the linear model that expressed a teams winning percentage as a linear function of is ERA. Use four decimals in each of your answers.Y^i = ? + - Xi(e) A certain professional baseball team had an earned run average of 3.45 this past…
2. Following data is amount of Assessed Value for an office building for a given floor area, number of office space, number of entrances, and the age of the offic building. Use excel to …. Obtain a Scatter plot of Floor Area as the independent and Assessed value as the dependent variable. Note the linear regression Model Predict the assessed value for 6000 sq ft. FloorArea (Sq.Ft.) Offices Entrances Age AssessedValue ($'000) 4790 4 2 8 1796 4720 3 2 12 1544 5940 4 2 2 2094 5720 4 2 34 1968 3660 3 2 38 1567 5000 4 2 31 1878 2990 2 1 19 949 2610 2 1 48 910 5650 4 2 42 1774 3570 2 1 4 1187 2930 3 2 15 1113 1280 2 1 31 671 4880 3 2 42 1678 1620 1 2 35 710 1820 2 1 17 678 4530 2 2 5 1585 2570 2 1 13 842 4690 2 2 45 1539 1280 1 1 45 433…
Using your favorite statistics software package, you generate a scatter plot with a regression equation and correlation coefficient. The regression equation is reported asy=20.41x+15.59y=20.41x+15.59and the r=0.272r=0.272.What proportion of the variation in y can be explained by the variation in the values of x?r² = %Report answer as a percentage accurate to one decimal place.
A movie studio wishes to determine the relationship between the revenue from rental of comedies on streaming services and the revenue generated from the theatrical release of such movies. The studio has the following bivariate data from a sample of fifteen comedies released over the past five years. These data give the revenue x from theatrical release (in millions of dollars) and the revenue y from streaming service rentals (in millions of dollars) for each of the fifteen movies. Also shown are the scatter plot and the least-squares regression line for the data. The equation for this line is y = 3.58 +0.15x. Theater revenue, x (in millions of dollars) 26.4 36.7 43.5 31.6 60.4 14.8 21.3 49.3 7.7 24.8 27.8 12.9 60.6 26.4 66.4 Send data to calculator V Rental revenue, y (in millions of dollars) 8.1 12.4 6.8 5.1 15.4 2.6 5.8 16.5 2.2 9.1 3.3 9.8 10.8 11.7 9.6 Based on the studio's data and the regression line, complete the following. Rental revenue in millions of dollars) 0 X 10 X 20…
Report the equation of the regression line and interpret it in the context of the problem
The invasive diatom species Didymosphenia geminata has the potential to inflict substantial ecological and economic damage in rivers. An article described an investigation of colonization behavior. One aspect of particular interest was whether y = colony density was related to x = rock surface area. The article contained a scatterplot and summary of a regression analysis. Here is representative data. x 50 71 55 50 33 58 79 26 y 157 1934 53 27 7 10 40 12 x 69 44 37 70 20 45 49 y 274 43 176 18 48 190 30 (a) Fit the simple linear regression model to this data. (Round your numerical values to three decimal places.) y = Predict colony density when surface area = 70 and calculate the corresponding residual. (Round your answers to the nearest whole number.) colony density corresponding residual Predict colony density when surface area = 71 and calculate the corresponding residual. (Round your answers to the nearest whole number.) colony…
We give the total variation, the unexplained variation (SSE), and the least squares point estimate b1 . Total variation = 13.459; SSE = 2.806; b1 = 2.6652 Click here for the Excel Data File Using the information given, find the explained variation, the simple coefficient of determination (r2), and the simple correlation coefficient (r). Interpret r2. (Round your answers to 3 decimal places. Round your percent to 1 decimal place.) Explained variation r2 r % of the variation in demand can be explained by variation in price differential.
The data show the number of viewers for television stars with certain salaries. Find the regression equation, letting salary be the independent (x) variable. Find the best predicted number of viewers for a television star with a salary of $6 million. Is the result close to the actual number of viewers, 8.9 million? Use a significance level of 0.05. Salary (millions of $) Viewers (millions) Click the icon to view the critical values of the Pearson correlation coefficient r. 98 3.5 3 7 13 12 13 10 2 6.8 6.3 10.2 8.5 4.4 1.8 2.7 What is the regression equation? y=+x (Round to three decimal places as needed.) What is the best predicted number of viewers for a television star with a salary of $6 million? The best predicted number of viewers for a television star with a salary of $6 million is million. (Round to one decimal place as needed.) Is the result close to the actual number of viewers, 8.9 million? O A. The result is very close to the actual number of viewers of 8.9 million. O B. The…
Listed below are paired data consisting of movie budget amounts and the amounts that the movies grossed. Find the regression equation, letting the budget be the predictor (x) variable. Find the best predicted amount that a movie will gross if its budget is $135 million. Use a significance level of alpha equals 0.05 . Budget left parenthesis $ right parenthesis in Millions 45 24 115 74 72 48 117 67 4 60 124 24 6 152 8 Gross left parenthesis $ right parenthesis in Millions 115 10 95 69 127 112 93 101 50 102 223 26 18 282 56 The regression equation is ŷ = __ + __x. (Round to one decimal place as needed.)
Listed below are paired data consisting of movie budget amounts and the amounts that the movies grossed. Find the regression equation, letting the budget be the predictor (x) variable. Find the best predicted amount that a movie will gross if its budget is $100100 million. Use a significance level of alpha equals 0.05α=0.05. Budget left parenthesis $ right parenthesisBudget ($)in Millionsin Millions 4242 2525 117117 6565 7575 4747 123123 6969 33 5959 122122 2020 1010 145145 1111 Gross left parenthesis $ right parenthesisGross ($) in Millionsin Millions 123123 2020 111111 6868 127127 110110 101101 103103 5050 113113 213213 2626 1717 285285 5555 LOADING... Click the icon to view the critical values of the Pearson correlation coefficient r. Question content area bottom Part 1 The regression equation is ModifyingAbove y with caretyequals=enter your response hereplus+enter your response…