Question

Eight people participated in a study examining the relationship between number of fast food stops and weight gain. The correlation coefficient was found to be .96, and the regression equation is 2.83 + 1.2x.

(A) With reference to the correlation coefficient, what can you conclude about the relationship between the number of fast food stops amount of weight gained?

(B) What is the slope of the line? Interpret the slope in words.

(C) The amount of weight gained can vary for a lot of reasons. How much of that variability is explained by the number of fast food stops?

(D) Could there be lurking variables in this case? Describe at least two that may impact this relationship.

(E) One of the individuals in the sample stopped 5 times per week but only recorded a five pound weight gain. Using the regression equation, predict the number of pounds gained we should see if someone stops 5 times per week, and then calculate the residual.

Answer 1

SolutionA

r=0.96

There exists a strong positive relationship between x and y

Form:linear

direction:positive

strength:strong

SolutionB:

y2.83 + 1.2x.

slope of the line=1.2

For unit increase in x ,y increases by 1.2

Solutionc:

r sq=r*r=0.96*0.96=0.9216

92.16% variation in y is explained by linear model.

Good model.

Solutione:

weight gain=2.83 + 1.2*number of fast food stop

Given number of fast food stop=5

Weight gain=2.83 + 1.2*5=8.83

predicted number of pounds gained=8.83

Residual =observed-predicted

=5-8.83

=-3.83

8.83 POUNDS

-3.83 POUNDS