Could someone answer this question so I understand it. The answer is 28.0, but i'd like to know how to do it. Thanks
Randomly selected cars were weighed, and the
highway fuel consumption amounts (in miles/gal) were determined. For 20 cars, the linear
correlation coefficient is found to be r = −0.874 and the equation of the regression line is ˆy
= 50.0 − 0.00628x, where x is the weight in pounds. Also, the 20 cars have a mean weight of
3232 lb and a mean highway fuel consumption amount of 29.7 mi/gal. What is the best
predicted value for the highway fuel consumption amount for a car that weighs 3500 lb?
To find the best predicted value for the highway fuel consumption amount for a car that weighs 3500 lb, you can use the equation of the regression line:
ŷ = b₀ + b₁x
In this case, b₀ = 50.0 and b₁ = -0.00628. Substitute these values into the equation:
ŷ = 50.0 - 0.00628x
Now, plug in the value of x = 3500 lb into the equation:
ŷ = 50.0 - 0.00628(3500)
ŷ = 50.0 - 21.98
ŷ ≈ 28.0
Therefore, the best predicted value for the highway fuel consumption amount for a car that weighs 3500 lb is approximately 28.0 miles/gallon.