12. Select the best interpretation of the slope of the least squares regression
ID: 3315148 • Letter: 1
Question
12. Select the best interpretation of the slope of the least squares regression equation. A. We predict the number of Tootsie rolls grabbed will increase by 1.17 on average for every 1 cm increase in hand span. B. We predict the hand span will increase by 1.17 cm on average for every 1 more Tootsie Roll grabbed. C. If a person grabs 0 Tootsie Rolls, we would predict their hand span would be 1.17 cm. D. If a person has a hand span of 0 cm, we would predict they would grab 1.17 Tootsie rolls. 13. Explain why an interpretation of the y-intercept does not make sense for these data. 14. [2 pts] Write a sentence interpreting the coefficient of determination (R2) in the context of the problem. 15. Use the least squares regression line to predict the number of Tootsie Rolls grabbed by someone with a hand span of 20 cm. 16. One of the subjects had a hand span of 20 cm and was recorded grabbing 16 Tootsie Rolls. Calculate the residual for this subject.
DATA:
Explanation / Answer
There are two variables as Hand Span and Tootsie Roll .
As the Hand Span increases , then number of tootsie roll increases .
That is number of tootsie roll depends on Hand span.
So, x variable is Hand span and y variable is tootsie roll.
From above data , slope 1.17
12 . Interpretation : We predict the number of Tootsie rolls grabbed will increase by 1.17 on average for every 1 cm increase in hand span.
13 . Intercept of the given data is -7.246, If we hav to interpret it , that means we have to say that if the hand Span is 0 then numbr of Tootsie Roll will be -7.246 , which has no meaning , so y-intercept does not make sense for these data .
14. For above data we got R2 = 0.33 .So we can say that there is 33% variation in number of Tootsie rolls due to Hand span .
15. From the above data we got regression quation as :
y^ = 1.17x - 7.246
We have given x = 20 , so y^ = 1.17*20 -7.246 = 16.154 = 17 .
16 . For x = 20 w predict number of tootsie roll = 17 that is y^ = 17 and we have given y = 16 for x = 20
So residual = y - y^ = 16 - 17 = -1
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