Ms. Ilene Over baked a cake. She removed the cake from her oven, put it in her c
ID: 3230508 • Letter: M
Question
Ms. Ilene Over baked a cake. She removed the cake from her oven, put it in her cake plate and left to cool in a room kept at a room temperature of 70oF. She measured the temperature of the cake every 10 minutes as recorded in the chart below. Ms. Over went to the fresh market while the cake was cooling. She returned home 2 hours (120 minutes later). Minutes out of oven, x Temperature of cake, y 10 181oF 20 158oF 30 140oF 40 126oF 50 114oF 60 105oF 2a. What is the equation of the line of best fit for the data? b. Interpret the slope of the line. c. Interpret the y-intercept of the line if appropriate d. According to the model, when will the cake cool to a temperature of 100oF? e. According to the model, what is the expected temperature of the cake after 1 hour and 15 minutes of cooling? f. Is the model valid for 2 hours after cooling? Why or why not?
Minutes out of oven, x
Temperature of cake, y
10
181oF
20
158oF
30
140oF
40
126oF
50
114oF
60
105oF
Minutes out of oven, x
Temperature of cake, y
10
181oF
20
158oF
30
140oF
40
126oF
50
114oF
60
105oF
Explanation / Answer
using Minitab:
Regression Analysis: y versus x
Analysis of Variance
Source DF Adj SS Adj MS F-Value P-Value
Regression 1 1193 1193 0.44 0.542
x 1 1193 1193 0.44 0.542
Error 4 10772 2693
Total 5 11965
Model Summary
S R-sq R-sq(adj) R-sq(pred)
51.8933 9.97% 0.00% 0.00%
Coefficients
Term Coef SE Coef T-Value P-Value VIF
Constant 81.3 48.3 1.68 0.168
x 0.83 1.24 0.67 0.542 1.00
Regression Equation
y = 81.3 + 0.83 x
Interpret the slope: If the Minutes out of oven increases by 1 minute, we predict the Temperature of cake will increase by approximately 0.83 yards.
Interpret the intercept. If the Minutes out of oven is 0 seconds, then we predict the Temperature of cake is 81.3.
d.
Variable Setting
x 100
Fit SE Fit 95% CI
163.838 83.3684 (-67.6298, 395.306)
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