**Educational Website Text**The accompanying data represent the weights of various domestic cars and their gas mileages in the city. The linear correlation coefficient between the weight of a car and its miles per gallon in the city is $ r = -0.983 $. The least-squares regression line treating weight as the explanatory variable and miles per gallon as the response variable is $ \hat{y} = -0.0075x + 46.5061 $. Complete parts (a) through (c) below.**(a)** What proportion of the variability in miles per gallon is explained by the relation between weight of the car and miles per gallon?The proportion of the variability in miles per gallon explained by the relation between weight of the car and miles per gallon is ______%. (Round to one decimal place as needed.)**(b)** Construct a residual plot to verify the requirements of the least-squares regression model. Choose the correct graph below.- **A**: A horizontal residual plot- **B**: A residual plot with a pattern- **C**: A random residual plot- **D**: A diagonal residual plot**(c)** Interpret the coefficient of determination and comment on the adequacy of the linear model.\[ \text{__}% \text{ of the variance in } y \text{ is } \_\_\_\_ \text{ by the linear model. The least-squares regression model appears to be } \_\_\_\_, \text{ based on the residual plot. \newline (Round to one decimal place as needed.)}\]**Data Table:**| Car | Weight (pounds), $ x $ | Miles per Gallon, $ y $ ||-------|--------------------------|--------------------------|| Car 1 | 3,765 | 18 || Car 2 | 3,984 | 17 || Car 3 | 3,530 | 21 || Car 4 | 3,175 | 23 || Car 5 | 2,550 | 21 || Car 6 | 3,730 | 18 || Car 7 | 2,605 | 26 || Car 8 | 3,772 | 17 || Car 9 | 3,310 | 21 || Car

Since you have asked multiple questions as per guideline we have solve first Question for you. Given, r2=0.983 Y^= -0.0075x+46.5061

Answered: The accompanying data represent the…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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you are going to buy some calves. What should a healthy weight be? let x be the age of the calf (in weeks), and let y be the weight of the calf (in kg) the calves you want to buy are 12 weeks old. Predict the healthy weight you should expect. x=1 3 10 16 26 36 y=42 50 75 100 150 200 state the correlation coefficient and regression line equation.
A study by Judge and Cable (2010) suggests that there is a positive relationship between weight and income for a group of men. The following data is similar to what was collected in the study. To simplify the weight variable, the men are categorized into five categories that measure actual weight relative to height from 1=thinnest to 5=heaviest. Income is recorded as thousands earned annually. Weight (X) Income (Y) 4 151 5 88 3 52 2 73 1 49 3 92 1 56 5 143 a. Calculate the Pearson correlation for these data. b. Is the correlation statistically significant? Use a two-tailed test with a=.05.
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The datasetBody.xlsgives the percent of weight made up of body fat for 100 men as well as other variables such as Age, Weight (lb), Height (in), and circumference (cm) measurements for the Neck, Chest, Abdomen, Ankle, Biceps, and Wrist. We are interested in predicting body fat based on abdomen circumference. Find the equation of the regression line relating to body fat and abdomen circumference. Make a scatter-plot with a regression line. What body fat percent does the line predict for a person with an abdomen circumference of 110 cm? One of the men in the study had an abdomen circumference of 92.4 cm and a body fat of 22.5 percent. Find the residual that corresponds to this observation. Bodyfat Abdomen 32.3 115.6 22.5 92.4 22 86 12.3 85.2 20.5 95.6 22.6 100 28.7 103.1 21.3 89.6 29.9 110.3 21.3 100.5 29.9 100.5 20.4 98.9 16.9 90.3 14.7 83.3 10.8 73.7 26.7 94.9 11.3 86.7 18.1 87.5 8.8 82.8 11.8 83.3 11 83.6 14.9 87 31.9 108.5 17.3…
The correlation between first year college GPA and high school GPA is 0.683. If a simple linear regression was conducted to predict first year college GPA from high school GPA what does the correlation tell us about the fit of the model?
The data show the chest size and weight of several bears. Find the regression equation, letting chest size be the independent (x) variable. Then find the best predicted weight of a bear with a chest size of 40 inches. Is the result close to the actual weight of 352 pounds? Use a significance level of 0.05. Chest size (inches) *Weight (pounds) 44 54 328 528 41 55 39 51 418 580 296 503 Click the icon to view the critical values of the Pearson correlation coefficient r. - What is the regression equation? x (Round to one decimal place as needed.)
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The table below shows the number of state-registered automatic weapons and the murder rate for several Northwestern states. X Y 11.4 8.6 7.2 3.6 13.5 11.3 10.1 x = thousands of automatic weapons y = murders per 100,000 residents 2.4 2.8 2.3 0.9 7 6.1 6.6 5.9 4.7 This data can be modeled by the equation y = 0.83x +4.06. Use this equation to answer the following; Special Note: I suggest you verify this equation by performing linear regression on your calculator. Answer = A) How many murders per 100,000 residents can be expected in a state with 2.7 thousand automatic weapons? Answer = Round to 3 decimal places. B) How many murders per 100,000 residents can be expected in a state with 11 thousand automatic weapons? Round to 3 decimal places.
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