9. The owner of a towing and garage service wants to know how the lowest tempera
ID: 3318671 • Letter: 9
Question
9. The owner of a towing and garage service wants to know how the lowest temperature on a winter day affects the number of emergency road service calls he receives. He records the lowest temperature (in 1°F) and the number of emergency road service calls he received onn-30 randomly selected winter days. Summary statistics of data are -= 15, s. = 16.6, y= 17.6, and S, = 8.3 a) In view of the question the owner wants to answer, what is the independent variable, and what is the response variable? Response/Dependent Variable: Explanatory/Independent Variable: b) Suppose that the correlation between the number of emergency road service calls and the lowest temperature was calculated to be r =0.88. Find the least squares regression equation, a= c) When the lowest temperature increases by 1°F, then on average, the number of emergency road service calls the owner receives will Increase / decrease by d) What is the predicted number of emergency calls he will receive when the lowest temperature is 15oF:Explanation / Answer
a) dependent variable - number of emergency road service calls
independent - lowest temperature
b) b^ = r sy/sx = 0.88*8.3/16.6 = 0.44
a =ybar -b*xbar = 17.6 - 0.44*4 = 11
hence
y^ = 11 +0.44*x
c) increase by 0.44
d) y^ = 11+0.44*15
= 17.6
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