Question

You are given the following regression equation for a scatter plot which The displays data Weight of Car (in pounds) and y = Miles per Gallon in City: for x = y = -0.006.0 + 42.825 p2 = 0.7496 (Note: The scatter plot graph is attached to the Canvas assignment as a separate document.) (a) Find the value of r based on the information given. (b) Based on your value of r, what conclusion can you make about the correlation of this data? (c) What does the value of p2 tell you about the regression? (d) Use the regression equation to estimate miles per gallon for a car that weighs 3000 pounds. (e) Use the regression equation to estimate the weight of a car that gets 30 miles per gallon.

Answer 1

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a) value of r = square root of r^2 = √(0.7496) = 0.8658

b) r indicates correlation coefficient between variable X (Weight of Car) and Y (Miles per Gallon).

correlation coefficient value of 0.8658 indicates that there is 86.58% correlation between weight of car and miles per gallon i.e. there is strong linear postive correlation between weight of car and miles per gallon.

c) r^2 value indicates coefficient of determination i.e. % of variation present in Y or dependent variable that is explained by independent variable/s

here r^2 = 0.7496 which indicates that 74.96% of variation present in Miles per Gallon variable is explained by Weight of Car variable.

d) Y = 42.825 - 0.006*X

X=3000

Y = 42.825 - 0.006*3000 = 24.825