MATH 225N Week 8 Assignment Coefficient of Determination
Compute and interpret the coefficient of determination
Question
A medical experiment on
... [Show More] tumor growth gives the following data table.
x y
57 38
61 50
63 76
68 97
72 113
The least squares regression line was found. Using technology, it was determined that the total sum of squares (SST) was 3922.8 and the sum of squares of regression (SSR) was 3789.0. Calculate R2, rounded to three decimal places.
CORRECT ANSWER:
0.966
Correct! You nailed it.
R2=SSRSST
R2=3789.03922.8
R2=0.966
Compute and interpret the coefficient of determination
Question
A scientific study on mesothelioma caused by asbestos gives the following data table.
Micrograms of asbestos inhaled Area of scar tissue (cm2)
58 162
62 189
63 188
67 215
70 184
Using technology, it was determined that the total sum of squares (SST) was 1421.2 and the sum of squares due to error (SSE) was 903.51. Calculate R2 and determine its meaning. Round your answer to four decimal places.
Correct answer:
R2=0.3643.
Great work! That's correct.
Therefore, 36.43% of the variation in the observed y-values can be explained by the estimated regression equation. R2=1−SSESST
R2=1−903.511421.2
R2=1−0.6357
R2=0.3643
R2=36.43%.
Compute and interpret the coefficient of determination
Question
A new mine opened and the number of dump truck loads of material removed was recorded. The table below shows the number of dump truck loads of material removed and the number of days since the mine opened.
Days (since opening) # of dump truck loads
2 45
5 53
8 60
9 60
12 67
A least squares regression line was found. Using technology, it was determined that the total sum of squares (SST) was 278.0 and the sum of squares of regression (SSR) was 274.3. Use these values to calculate the coefficient of determination. Round your answer to three decimal places. 0.987.
Yes that's right. Keep it up!
R2=SSRSST
R2=274.3278.0
R2=0.987
Compute and interpret the coefficient of determination
Question
A new mine opened and the number of dump truck loads of material removed was recorded. The table below shows the number of dump truck loads of material removed and the number of days since the mine opened
Days (since opening) # of dump truck loads
6 54
9 78
14 92
17 86
21 121
A least squares regression line was found. Using technology, it was determined that the total sum of squares (SST) was 2349 and the sum of squares of error (SSE) was 329. Use these values to calculate the coefficient of determination. Round your answer to three decimal places.
CORRECT ANSWER: 0.860.
Yes that's right. Keep it up!
R2=1−SSESST
R2=1−3292349
R2=1−0.140
R2=0.860 [Show Less]