Description
MATH225N Week 8 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 |
The 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.
Ans: 0.987
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.
Ans: R2=0.3643
Question
A scientific study on fishing gives the following data table.
| Fishing Lines | Fish Caught |
| 4 | 13 |
| 5 | 15 |
| 7 | 25 |
| 11 | 29 |
| 12 | 26 |
Using technology, it was determined that the total sum of squares (SST) was 203.20 and the sum of squares due to error (SSE) was 41.62. Calculate R2 and determine its meaning. Round your answer to four decimal places.
SOLUTION:
Coefficient of Determination
Understanding R²
The coefficient of determination (R2R^2) is a statistical measure that shows how well the independent variable(s) explain variation in the dependent variable. It is defined as the proportion of the total variability in the response variable (yy) that is explained by the regression model (Triola, 2018). Mathematically,
R2=SSRSST=1−SSESST,R^2 = \frac{SSR}{SST} = 1 – \frac{SSE}{SST},
where SST is the total sum of squares, SSR is the sum of squares due to regression, and SSE is the sum of squares due to error (Bluman, 2017).
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An R2R^2 close to 1 indicates that most of the variability is explained by the model.
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An R2R^2 close to 0 means the model explains little of the variability.…………………………Get a complete solution at $ 9.99
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