1. You are given the following statistics: means, standard deviations and correl

Question

1. You are given the following statistics: means, standard deviations and correlations for 4 variables The four variables are miles per gallon, weight of car, front profile (1-Low, O-Not Low) and the manufacturer's suggested retail price. Answer the questions that follow MPG 25 Weight 2500 200 Low Profile Front 60 45 MSRP 18,000 6,000 Means St Dev MPG 1.0 60 Weight Low Profile Front Correlations MPG Weight Low Profile Front 25 MSRP MSRP 1.0 30 20 1.0 30 05 1.0 Which costs more, (low or high) front profile vehicles Best predictor of MPG is Heavier cars have a (low or high) profile front High MPG vehicles have 'significantly' higher prices than low MPG vehicles(T/F) Weakest predictor of MPG is Slope of the line for MPG against Low Profile Front would be (Pos, Neg or zero) C. f. Slope of the line for MPG against Low Profile front is 5. Interpret this slope relative to the two variables

Explanation / Answer

a) From the table, it can be seen that there is a relationship of 0.3 between Low Profile Front and MSRP.This indicates that Low Profile Front and MSRP are positively related in terms of price. Hence, Low Profile Vehicles are more expensive than High Profile Vehicles

b) The best predictor of MPG is weight as it has the highest correlation value(consider absolute value, ie, |-0.6|).

c) There is a negative correlation between weight and low profile front(-0.3). This means that as weight increases,profile score decreases. As per the question, profile score of 0 indicates High. Thus, heavier cars have higher profile.

d) The correlation value between MSRP and MPG is .05, which is weak.So, high MPG vehicles wont have significantly higher prices than low MPG vehicles. The answer is False

e) The weakest predictor of MPG is MSRP as it has the smallest correlation value(0.05).

f) Slope of line for MPG against Low Profile Front will be positive, since the correlation value is positive(0.25)

g) Slope of 2 variables x,y indicates change in y due to change in x. Front profile variable has only 2 values , 1-Low, 0-High. Given, slope of MPG against Low Profile Front is 5.

This means that Low profile cars average 5 MPG more than High Profile Cars.

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