After keeping track of his heating expenses for several winters, a homeowner bel
ID: 2930293 • Letter: A
Question
After keeping track of his heating expenses for several winters, a homeowner believes he can estimate the monthly cost from the average daily Fahrenheit temperature using the model cost (with a hat on top) = 105 - 1.82 temp. Complete parts (a) through (g) below.
a) Interpret the slope of the line in this context. What does the model predict given a 1° increase in temperature?
A.
The model predicts a $105 decrease in heating cost.
B.
The model predicts a $105 increase in heating cost.
C.
The model predicts a $1.82 decrease in heating cost.
D.
The model predicts a $1.82 increase in heating cost.
b) Interpret the y-intercept of the line in this context. What does the model predict given a temperature of 0°?
A.
The model predicts a heating cost of $0.
B.
The model predicts a heating cost of $1.82.
C.
The model predicts a heating cost of $105.
D.
The model predicts a heating cost of $50.
c) During the months when the temperature stays around freezing (32° F), would you expect the cost predictions based on the model to be accurate, too low, or too high? Explain.
A.
Too low comma because the residual of the value at 32 degrees is positive.
B.
Accurate comma because the predicted and observed values at 32 degrees are very close.
C.
Accurate, because the residual of the value at 32 degrees is positive.
D.
Too high comma because the residual of the value at 32 degrees is negative.
d) What heating cost does the model predict for a month that averages 10°?
Cost (with a hat on top) = $ (Round to the nearest cent as needed.)
e) During one of the months on which the model is based, the temperature did average 10°. What were the actual heating costs for this month?
The actual heating costs for this month were $. (Round to the nearest dollar as needed.)
f) Do you think the homeowner should use this model? Explain.
No,
Yes,
because the plot of the residuals
shows
does not show
a pattern.
g) Would this model be more successful if created using degrees Celsius? Explain.
A.
Yes, because the residuals would be scaled down to smaller values.
B.
No, because units do not influence the accuracy of a regression.
C.
Yes, because Celsius degrees are larger than Fahrenheit degrees.
D.
No, because using Celsius would make the model less successful.
10 5 0 1p 20 30 40 -5 10 15- 20 Average TemperatureExplanation / Answer
a)
cost = 105-1.82 temp
This indicates that the slope is (-1.82), that means as the temperature increases the cost decreases.
In particular for every degree dip in temperature the cost decreases by 1.82 dollars.
When the temperature dips by 1 degree,
cost = 105 - 1.82 * 1 = 103.18
Therefore the cost has decreasd by 1.82. Answer is
C.
The model predicts a $1.82 decrease in heating cost.
b)
y-intercept in the line is 105. This means the cost starts at 105 dollars for 0 degrees and keeps dipping from this foe every degree increase in temperature.
When the temperature is 0 degrees,
cost = 105 - 1.82*0 = 105
Answer is
C.
The model predicts a heating cost of $105.
c) From the graph, note that the residual is negative for 32 degrees (30-40 degrees).
Residual = original value - predicted value
when residual is negative it indicates that the predicted value is higher than the original value.
Answer is
D.
Too high comma because the residual of the value at 32 degrees is negative.
d) According to the model when the average temperature is 10 degrees,
cost = 105 - 1.82*10 = 105 - 18.2 = 86.8 dollars.
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