Description
Week 8: Regression
Week | Assignments | Due Date |
Week 8 | Graded Discussion | Suggested Due Date—
Initial Post: Wednesday of Week 8
Due Date— Responses: Sunday of Week 8 [Have two posts on two different days] |
Knewton Homework Assignments
Coefficient of Determination Correlation and Causation Linear Regression Equations Performing Linear Regressions with Technology – Excel Predictions Using Linear Regression |
Sunday of Week 8 | |
Week 8 final exam |
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Week 8 Assignment – Coefficient of Determination
Activity 1
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.
Answer
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Activity 2
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:
Answer
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Activity 3
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.
Answer
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Activity 4
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.
Answer
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Activity 5
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:
- 987
- 013
- 993
Answer
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Activity 6
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:
- 860
- 140
- 000
Answer
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