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The manager of a used-car dealership is very interested in the resale price of used cars. The manager feels that the age of the car (x) is important in determining the resale value (y). He collects data on the age and resale value of 15 cars and runs a regression analysis with the value of the car (in thousands of dollars) as the response variable and the age of the car (in years) as the predictor variable. He found that the mean age of the used car in the sample is about 14 years and the standard deviation is about 2.6 years. The sample mean price is 17 with a standard deviation of 4. The correlation between age of cars and the prices is about -0.4. a) The slope of the regression line of yield of price on age is: b) The intercept of the regression line of yield of price on age is: c) The predicted value of the price of a used car which is 13 years old is: d) Suppose a certain used car of age 13 years is sold at a price of 2.1. The residual value of the price is: e) What percentage of the total sample variation in price is explained by the model?

          The manager of a used-car dealership is very interested in the resale price of used cars. The manager feels that the age of the car (x) is important in determining the resale value (y). He collects data on the age and resale value of 15 cars and runs a regression analysis with the value of the car (in thousands of dollars) as the response variable and the age of the car (in years) as the predictor variable. He found that the mean age of the used car in the sample is about 14 years and the standard deviation is about 2.6 years. The sample mean price is 17 with a standard deviation of 4. The correlation between age of cars and the prices is about -0.4.

a) The slope of the regression line of yield of price on age is:
b) The intercept of the regression line of yield of price on age is:
c) The predicted value of the price of a used car which is 13 years old is:
d) Suppose a certain used car of age 13 years is sold at a price of 2.1. The residual value of the price is:
e) What percentage of the total sample variation in price is explained by the model?

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Elementary Statistics a Step by Step Approach

Allan G. Bluman 9th Edition

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Solved by Expert Sheryl Ezze

05/31/2022

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4 \times \left( \frac{4}{2.6} \right) = -0.6154 \] ** Show more…

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The manager of a used-car dealership is very interested in the resale price of used cars. The manager feels that the age of the car (x) is important in determining the resale value (y). He collects data on the age and resale value of 15 cars and runs a regression analysis with the value of the car (in thousands of dollars) as the response variable and the age of the car (in years) as the predictor variable. He found that the mean age of the used car in the sample is about 14 years and the standard deviation is about 2.6 years. The sample mean price is 17 with a standard deviation of 4. The correlation between age of cars and the prices is about -0.4. a) The slope of the regression line of yield of price on age is: b) The intercept of the regression line of yield of price on age is: c) The predicted value of the price of a used car which is 13 years old is: d) Suppose a certain used car of age 13 years is sold at a price of 2.1. The residual value of the price is: e) What percentage of the total sample variation in price is explained by the model?

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Transcript

00:01 So we have 15 pieces of data, and we know that the x data has a mean of 14 years with 2 .6 year standard deviation, and that's our age.

00:12 And the resale value in thousands has a mean of 17 or 17 ,000 and a standard deviation of four or $4 ,000.

00:19 And the correlation coefficient is negative 0 .4.

00:23 So as age increases, the resale decreases, as one would expect.

00:30 And we want to find the slope, first of all, and we know that the slope is the correlation coefficient times the standard deviation of y divided by the standard deviation of x.

00:43 And that's actually unit -wise that would be in dollars, actually thousands of dollars per year.

00:50 And this value comes out to be negative 0 .6154.

00:57 Now, we know that the point, 1417, the x bar, y bar point will be on the line.

01:06 And here's our line.

01:08 And we know that when we plug in the x bar and the y bar, that that equation will be true.

01:15 And we've just calculated what this slope is right here.

01:19 So now we can determine by plugging in our numbers what the intercept is, which is little a.

01:26 So a will equal the y bar minus the slope we just found times the x bar.

01:33 So it's going to equal the y bar 17 minus the slope of negative 0 .6154 times the x bar, which was, let's go back up and peak, is 14.

01:49 And so let's just double check.

01:52 I did the calculation before, but we're going to double check and make sure i didn't make mistakes.

01:55 17 minus negative 0 .6154 times 14.

02:02 Yes, and i get the y intercept to be the a value.

02:05 We'll just put that up here.

02:07 The a value, the y intercept is 25 .61, and we'll round it to five.

02:15 It rounds about five...

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