please show steps and explain! A study was done to evaluate the relationship bet
ID: 3155566 • Letter: P
Question
please show steps and explain!
A study was done to evaluate the relationship between highway miles per gallon (MPG) and vehicle weight (in pounds) for a sample of vehicles for sale at a certain dealership for a random sample of vehicles, the highway MPG and weight was measured. The least squares regression line was computed to be: Highway MPG= 45.69-0.0053 (weight) Predict the highway MPG for a vehicle weighing 3000 pounds: 24,49 mpg 29.79mpg 45.69mpg 53 mpg 319,271 61,59mpg What is the predicted change in the highway MPG for a 100 pound increase in weight? Highway MPG is predicted to decrease by 0.0053 mpg Highway MPG is predicted to decrease by 0.53 Highway MPG is predicted to decrease by 5.3 Highway MPG is predicted to increase by 0.0053 Highway MPG is predicted to increase by 0.53 Which of the following statements about the correlation coefficient, r, between highway MPG and vehicle weight is true? Since the slope is close to 0 then r must be close to 0 as well Since the slope is positive, r must be also positive Since the slope is negative r must be also negative A and B A and cExplanation / Answer
THE REGRESSION LINE GIVEN AS
Y = 45.69 - 0.0053 X
A) X = 3000, WE NEED TO FIND Y
THEREFORE
Y = 45.69 - 0.0053*3000
THEREFORE Y = 29.79
THEREFORE OPTION B IS CORRECT
B) AS THE WEIGHT WILL INCREASE
THE MPG WILL DECREASE
AS THE WIGHT HAS INCREASED BY 100
THEN MPG WILL DECREASE BY = 0.0053*100 = 0.53
THEREFORE OPTION B IS CORRECT
C) AS THE SLOPE IS POSITIVE THERE FORE R MUST BE POSITIVE THEREFORE OPTION B IS CORRECT
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