SOLUTION: I was wondering if I could get some help with this problem. A regression was done for 20 cities with latitude as the explanatory variable (x) and average January temperature as

Question 327288: I was wondering if I could get some help with this problem.
A regression was done for 20 cities with latitude as the explanatory variable (x) and average January temperature as the response variable (y). The latitude is measured in degrees and average January temperature in degrees Fahrenheit. The latitudes ranged from 26 (Miami) to 47 (Duluth) The regression equation is
y = 49.4 - 0.313x
The city of Miami, Florida has latitude 26 degrees with average January temperature of 67 degrees Fahrenheit.
1. What is the estimated average January temperature for Miami, and
2. based on the regression equation, what is the residual?
A) Estimated January temperature is 36.88 and the residual is 11.88
B) Estimated January temperature is 41.3 and the residual is - 25.7
C) Estimated January temperature is 36.88 and the residual is - 11.88
D) Estimated January temperature is 41.3 and the residual is 25.7
I am at a loss trying to figure this out.
Thanks,
Dave
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
A regression was done for 20 cities with latitude as the explanatory variable (x) and average January temperature as the response variable (y).
-------------------------------------------
The latitude is measured in degrees and average January temperature in degrees Fahrenheit. The latitudes ranged from 26 (Miami) to 47 (Duluth) The regression equation is T(x) = 49.4 - 0.313x
================================================
The city of Miami, Florida has latitude 26 degrees with average January temperature of 67 degrees Fahrenheit.
1. What is the estimated average January temperature for Miami?
T(26) = 49.4-0.313(26) = 41.26
------------------------------
2. based on the regression equation, what is the residual?
Residual = Observed-Estimated = 67-41.26 = 25.74
------------------------------
Cheers,
Stan H.
====================================
A) Estimated January temperature is 36.88 and the residual is 11.88
B) Estimated January temperature is 41.3 and the residual is - 25.7
C) Estimated January temperature is 36.88 and the residual is - 11.88
D) Estimated January temperature is 41.3 and the residual is 25.7
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