Question

Daniel really wanted to purchase a Chevrolet Impala. He gathered data on 20 Impalas from www.carmax.com and found the mean mileage to be 50,400 miles with a standard deviation of 27,503.88 miles. The mean price of the 20 Impalas was $13,228.30 with a standard deviation of $1,942.63. The correlation between mileage and price was –0.912. Calculate the equation of the least-squares regression line for predicting the price from mileage.

Answer 1

The equation of the least-squares regression line for predicting the price from mileage is y = -0.064x + 16219.78.

Step-by-step explanation:

To calculate the equation of the least-squares regression line, we need to use the formula: y = bx + a, where y is the predicted price, x is the mileage, b is the slope of the line, and a is the y-intercept.

The slope of the line can be calculated using the formula: b = r * (sd_y / sd_x), where r is the correlation between mileage and price, sd_y is the standard deviation of the price, and sd_x is the standard deviation of the mileage.

Plugging in the given values:

b = -0.912 * (1942.63 / 27503.88) = -0.064

To find the y-intercept a, we can use the formula: a = mean_y - (b * mean_x), where mean_y is the mean price and mean_x is the mean mileage.

Plugging in the given values:

a = 13228.30 - (-0.064 * 50400) = 16219.78

Therefore, the equation of the least-squares regression line for predicting the price from mileage is: y = -0.064x + 16219.78.