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Calculate, test, and interpret the relationship between two variables using the correlation coefficient

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The owner of Maumee Ford-Mercury-Volvo wants to study the relationship between the age of a car and its selling price. Listed below is a random sample of 12 used cars sold at the dealership during the last year.

Car Age (years) Selling Price ($000) Car Age (years) Selling Price ($000)
1 12 10.3 7 12 8.0
2 10 9.2 8 16 7.8
3 15 4.6 9 14 7.8
4 18 4.2 10 18 4.3
5 12 5.1 11 8 10.0
6 10 11.6 12 8 8.8

(a) Determine the regression equation. (Round your answers to 3 decimal places. Negative values should be indicated by a minus sign.)
a =
b =

(b) Estimate the selling price of a 13-year-old car (in $000). (Round your answer to 3 decimal places.)
Selling price =

(c) Interpret the regression equation (in dollars). (Round your answer to nearest dollar amount.)
For each additional year, the car decreases $_____ in value.

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Solution Preview

Hi there,

Thanks for letting me work on your post. Here is my explanation:

mean of years (x) = (12+10+...+8)/12= 12.75
mean of ...

Solution Summary

The expert interprets the relationship between two variables.

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I need help (step-by-step) with the following questions for my upcoming test. (please see attached). Please explain the process of figuring these questions out. I have an upcoming final and I need to know how to do these problems.

A random sample of eight quarterback listed in The Sports Encyclopedia: Pro Football, gave the following information.

Let x = height of a quarterback in inches, and let y = weight of a quarterback in pounds.
x 75 78 74 73 72 75 76 73
y 205 230 210 210 195 215 203 196

a) Draw a scatter plot.
b) Calculate the correlation coefficient
c) Make a conclusion based upon the correlation coefficient.
d) Calculate the equation of the regression line and draw the line in your scatter plot.
e) If a quarterback is x = 76 inches tall, what can you predict is the weight of this quarterback?
f) Calculate the coefficient of determination.
g) Interpret the coefficient of determination in terms of your data.
h) Calculate the stand error of the estimate.
i) Interpret the standard error of the estimate in terms of your data.
j) Construct a 95% prediction interval for the weight of the quarterback when the height is 70 inches and interpret the results.

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