What is meant when a statistician talks about getting a "best fit" least squares regression line (hint: what is the mathematical relationship behind this?)
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What is meant when a statistician talks about getting a "best fit" least squares regression line (hint: what is the mathematical relationship behind this?)
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- An engineer wants to determine how the weight of a gas-powered car, x, affects gas mileage, y. The accompanying data represent the weights of various domestic cars and their miles per gallon in the city for the most recent model year. Complete parts (a) through (d) below. LOADING... Click here to view the weight and gas mileage data. Question content area bottom Part 1 (a) Find the least-squares regression line treating weight as the explanatory variable and miles per gallon as the response variable. ModifyingAbove y with caretyequals=negative 0.00756−0.00756xplus+(44.844.8) (Round the x coefficient to five decimal places as needed. Round the constant to one decimal place as needed.) Part 2 (b) Interpret the slope and y-intercept, if appropriate. Choose the correct answer below and fill in any answer boxes in your choice. (Use the answer from part a to find this answer.) A. For every pound added to the weight of the car, gas mileage in the…(b)An engineer wants to determine how the weight of a gas-powered car, x, affects gas mileage, y. The accompanying data represent the weights of various domestic cars and their miles per gallon in the city for the most recent model year. Complete parts (a) through (d) below. LOADING... Click here to view the weight and gas mileage data. Question content area bottom Part 1 (a) Find the least-squares regression line treating weight as the explanatory variable and miles per gallon as the response variable. ModifyingAbove y with caretyequals=enter your response herexplus+(enter your response here) (Round the x coefficient to five decimal places as needed. Round the constant to one decimal place as needed.)
- 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.A pediatrician wants to determine the relation that exists between a child's height, x, and head circumference, y. She randomly selects 11 children from her practice, measures their heights and head circumferences, and obtains the accompanying data. Complete parts (a) through (g) below. Click the icon to view the children's data. Data table (a) Find the least-squares regression line treating height y =x+ (O (Round the slope to three decimal places and round the d Height (inches), x Head Circumference (inches), y O. 28 17.6 24.5 17.1 25.75 17.1 25.75 17.5 24.25 17.0 27.75 17.7 26.5 17.3 27.25 17.6 26.5 17.3 26.5 17.5 27.75 17.6 Print Done Help me solve this View an example Get more help - Media - Clear all Check answerA 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…
- An article gave a scatter plot along with the least squares line of x = rainfall volume (m3) and y = runoff volume (m3) for a particular location. The accompanying values were read from the plot. x 6 12 14 20 23 30 40 50 55 67 72 79 96 112 127 y 4 10 13 15 15 25 27 46 38 46 53 74 82 99 104 (a) Does a scatter plot of the data support the use of the simple linear regression model? Yes, the scatterplot shows a reasonable linear relationship.Yes, the scatterplot shows a random scattering with no pattern. No, the scatterplot shows a reasonable linear relationship.No, the scatterplot shows a random scattering with no pattern. (b) Calculate point estimates of the slope and intercept of the population regression line. (Round your answers to four decimal places.) slope intercept (c) Calculate a point estimate of the true average runoff volume when rainfall volume is 50. (Round your answer to four decimal places.) m3(d) Calculate a point estimate of the…A manager at the Camden Walmart is interested in learning more about the relationship between the number of customers in a checkout line and the total time it takes to check out. She selects a random sample of 11 customers and measured the number of customers who were in front of the selected customer in line and the time until that customer had finished checking out. An analysis of the data is provided below. Identify and interpret the y-intercept of the least squares regression line in context. Identify the coefficient of determination, r2. Interpret it in context. One of the data points appears to be an outlier. Describe this point and explain why it is considered an outlier.A chemical engineer is investigating the effect of process operating temperature on product yield. The study results in the following data: Temperature Yield 100 57.71 110 63.17 120 76.30 130 73.30 140 89.07 150 91.17 160 170 114.11 106.33 180 190 114.38 124.07 You can use Minitab to answer the following questions. However, you should be able to calculate the slope and intercept of the least squares regression model by hand, which requires only the mear and standard deviations of X and Y, and the correlation coefficient (here r = 0.9751). 1. what is the mean temperature? 155 150 130 145 Submit Answer Tries 0/2
