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(CORRECT ANSWER) MATH225N Week 8 Assignment : Coefficient of Determination

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Question

A scientific study on construction delays gives the following data table.

Construction delay (hours) Increased cost ($1000)
51 104
55 103
58 89
61 56
63 52

 

Using technology, it was determined that the total sum of squares (SST) was 2542.8, the sum of squares regression (SSR) was 2194.8, and the sum of squares due to error (SSE) was 347.99. Calculate R2 and determine its meaning. Round your answer to four decimal places.

Select the correct answer below:

R2=0.8631

Therefore, 86.31% of the variation in the observed y-values can be explained by the estimated regression equation.

R2=1.1586

Therefore, 1.1586% of the variation in the observed y-values can be explained by the estimated regression equation.

R2=0.1369

Therefore, 13.69% of the variation in the observed y-values can be explained by the estimated regression equation.

R2=0.1586

Therefore, 15.86% of the variation in the observed y-values can be explained by the estimated regression equation.

Question

A medical experiment on 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.

Provide your answer below:

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.

Select the correct answer below:

R2=0.3643

Therefore, 36.43% of the variation in the observed y-values can be explained by the estimated regression equation.

R2=0.3643

Therefore, 0.3643% of the variation in the observed y-values can be explained by the estimated regression equation.

R2=0.6357

Therefore, 63.57% of the variation in the observed y-values can be explained by the estimated regression equation.

R2=0.6357

Therefore, 0.6357% of the variation in observed y-values can be explained by the estimated regression equation.

Question

A scientific study on speed limits gives the following data table.

Average speed limit Average annual fatalities
25 16
27 29
29 38
32 71
35 93

Using technology, it was determined that the total sum of squares (SST) was 4029.2, the sum of squares regression (SSR) was 3968.4, and the sum of squares due to error (SSE) was 60.835. Calculate R2 and determine its meaning. Round your answer to four decimal places

Select the correct answer below:

R2=0.0153

Therefore, 1.53% of the variation in the observed y-values can be explained by the estimated regression equation.

R2=0.9849

Therefore, 98.49% of the variation in the observed y-values can be explained by the estimated regression equation.

R2=0.0151

Therefore, 1.51% of the variation in the observed y-values can be explained by the estimated regression equation.

R2=1.0153

Therefore, 10.153% of the variation in the observed y-values can be explained by the estimated regression equation.

R2=0.9849

Therefore, 98.49% of the variation in the observed y-values can be explained by the estimated regression equation.

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

Select the correct answer below:

0.987

0.013

0.993

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

Select the correct answer below:

0.860

0.140

2020.000

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