A well-educated lumberjack decides to use linear regression to predict the demand for firewood based on the ambient temperature. He has collected data on firewood sales and temperature for the last several days and has performed some preliminary calculations as shown in the table. What is his regression equation based on the data? $$\begin{array} { | c | c | c | c | c | }
\hline & \text { Temp } & \text { Ricks } & \text { Temp Squared } & \text { Temp *\# Ricks } \
\hline & 33 & 17 & 1089 & 561 \
\hline & 19 & 32 & 361 & 608 \
\hline & 34 & 20 & 1156 & 680 \
\hline & 34 & 18 & 1156 & 612 \
\hline & 20 & 33 & 400 & 660 \
\hline & 24 & 30 & 576 & 720 \
\hline & 17 & 34 & 289 & 578 \
\hline & 30 & 25 & 900 & 750 \
\hline & 38 & 16 & 1444 & 608 \
\hline & 23 & 29 & 529 & 667 \
\hline \text { Sums } & 272 & 254 & 7900 & 6444 \
\hline
\end{array}$$
A)Ricks = 50.6 - 0.93 × Temp
B)Temp = 53.3 - 1.0 × Ricks
C)Ricks = 0.93 - 50.6 × Temp
D)Temp = 1.0 - 53.3 × Ricks

Question

A well-educated lumberjack decides to use linear regression to predict the demand for firewood based on the ambient temperature. He has collected data on firewood sales and temperature for the last several days and has performed some preliminary calculations as shown in the table. What is his regression equation based on the data? $$\begin{array} { | c | c | c | c | c | } 
\hline & \text { Temp } & \text { Ricks } & \text { Temp Squared } & \text { Temp *\# Ricks } \
\hline & 33 & 17 & 1089 & 561 \
\hline & 19 & 32 & 361 & 608 \
\hline & 34 & 20 & 1156 & 680 \
\hline & 34 & 18 & 1156 & 612 \
\hline & 20 & 33 & 400 & 660 \
\hline & 24 & 30 & 576 & 720 \
\hline & 17 & 34 & 289 & 578 \
\hline & 30 & 25 & 900 & 750 \
\hline & 38 & 16 & 1444 & 608 \
\hline & 23 & 29 & 529 & 667 \
\hline \text { Sums } & 272 & 254 & 7900 & 6444 \
\hline
\end{array}$$
A)Ricks = 50.6 - 0.93 × Temp
B)Temp = 53.3 - 1.0 × Ricks
C)Ricks = 0.93 - 50.6 × Temp
D)Temp = 1.0 - 53.3 × Ricks

Quizplus · Accepted Answer

The regression equation will be of the form Ricks = a + b × Temp. Using the information given in the table, we can calculate the values for a and b using the formulas:

b = [nΣ(Temp × #Ricks) - Σ(Temp)Σ(#Ricks)] / [nΣ(Temp^2) - (Σ(Temp))^2]
a = (Σ(#Ricks) - bΣ(Temp)) / n

where n is the number of data points. Plugging in the values from the table, we get:

b = [10(6444) - (272)(254)] / [10(7900) - (272)^2] ≈ -0.93
a = (254 - (-0.93)(272)) / 10 ≈ 50.6

So the regression equation is Ricks = 50.6 - 0.93 × Temp.

A Well-Educated Lumberjack Decides to Use Linear Regression to Predict