A data set auto stores information about 392 car models including various performance specifications. You may...

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A data set auto stores information about 392 car models including various performance specifications. You may assume the data set is a simple random sample of autos from a much larger population. It has one row for each auto and contains four columns: name: the make and model of the auto year: the last two digits of the year the auto was made mpg: the fuel efficiency of the auto in miles per gallon horsepower: a measure of how powerful the engine is 225 200 175 name year mpg horsepower chevrolet chevelle malibu 70 buick skylark 320 plymouth satellite amc rebel sst 2222 18 130 70 15 165 horsepower 150 125 100 70 18 150 75 70 16 150 50 10 20 30 (388 rows omitted) mpg The column 'mpg' has mean 23 and standard deviation 7.8. The column 'horsepower' has mean 104 and standard deviation 38. The two columns have a correlation of -0.8. Suppose an analyst forgets what we know about not fitting linear regressions to nonlinear scatter plots, and uses a linear regression to estimate a line of equation of the form: predicted horsepower = slope * mpg + intercept. What is the slope of the regression line in standard units? (Make sure to justify your answer by writing the correct equation for the slope of the regression line and computing the answer correctly.) A data set auto stores information about 392 car models including various performance specifications. You may assume the data set is a simple random sample of autos from a much larger population. It has one row for each auto and contains four columns: name: the make and model of the auto year: the last two digits of the year the auto was made mpg: the fuel efficiency of the auto in miles per gallon horsepower: a measure of how powerful the engine is 225 200 175 name year mpg horsepower chevrolet chevelle malibu 70 buick skylark 320 plymouth satellite amc rebel sst 2222 18 130 70 15 165 horsepower 150 125 100 70 18 150 75 70 16 150 50 10 20 30 (388 rows omitted) mpg The column 'mpg' has mean 23 and standard deviation 7.8. The column 'horsepower' has mean 104 and standard deviation 38. The two columns have a correlation of -0.8. Suppose an analyst forgets what we know about not fitting linear regressions to nonlinear scatter plots, and uses a linear regression to estimate a line of equation of the form: predicted horsepower = slope * mpg + intercept. What is the slope of the regression line in standard units? (Make sure to justify your answer by writing the correct equation for the slope of the regression line and computing the answer correctly.)