Q1
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
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.
Q2
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.
Q3
A scientific study on lift strength gives the following data table.
| Lift strength (Tons) | Time to move load (seconds) |
| 46 | 159 |
| 47 | 166 |
| 51 | 123 |
| 55 | 128 |
| 56 | 117 |
Using technology, it was determined that the total sum of squares (SST) was 1989.2, the sum of squares regression (SSR) was 1598.1, and the sum of squares due to error (SSE) was 391.10. Calculate R2 and determine its meaning. Round your answer to four decimal places.
Ans:
R2=0.2447
Therefore, 24.47% of the variation in the observed y-values can be explained by the estimated regression equation.
R2=0.1966
Therefore, 19.66% of the variation in the observed y-values can be explained by the estimated regression equation.
R2=0.8034
Therefore, 80.34% of the variation in the observed y-values can be explained by the estimated regression equation.
R2=1.2447
Therefore, 12.447% of the variation in the observed y-values can be explained by the estimated regression equation.
Q4
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.
Ans:
0.860
0.140
2020.000
Q5
A scientific study on vine growth rates gives the following data table.
| Amount of fertilizer | Longest vine distance |
| 15 | 88 |
| 15 | 101 |
| 18 | 116 |
| 20 | 93 |
| 21 | 122 |
Using technology, it was determined that the total sum of squares (SST) was 854, the sum of squares regression (SSR) was 257.18, and the sum of squares due to error (SSE) was 596.82. Calculate R2 and determine its meaning. Round your answer to four decimal places.
Ans:
R2=0.6989
Therefore, 69.89% of the variation in the observed y-values can be explained by the estimated regression equation.
R2=0.3011
Therefore, 30.11% of the variation in the observed y-values can be explained by the estimated regression equation.
R2=3.3200
Therefore, 3.32% of the variation in observed y-values can be explained by the estimated regression equation.
R2=2.3200
Therefore, 2.32% of the variation in the observed y-values can be explained by the estimated regression equation.
Q6
A fishing enthusiast puts out different numbers of lines at once on several fishing trips to the same location and records the number of fish he catches on each trip. The table below shows the number of lines and number of fish caught on his trips.
| 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 of error (SSE) was 41.62. Use these values to calculate the coefficient of determination.
Ans:
0.7952
0.2049
161.5
0.3825
Q7
A scientific study on citizens who live to over 100 years of age gives the following data table.
| Age of patient | Loss of bone density |
| 101 | 73 |
| 102 | 86 |
| 105 | 118 |
| 108 | 109 |
| 111 | 121 |
Using technology, it was determined that the total sum of squares (SST) was 1761.2, the sum of squares regression (SSR) was 1302.3, and the sum of squares due to error (SSE) was 458.89. Calculate R2 and determine its meaning. Round your answer to four decimal places.
Ans:
R2=0.3524
Therefore, 35.24% of the variation in the observed y-values can be explained by the estimated regression equation.
R2=0.7394
Therefore, 73.94% of the variation in the observed y-values can be explained by the estimated regression equation.
R2=0.2606
Therefore, 26.06% of the variation in the observed y-values can be explained by the estimated regression equation.
R2=1.3524
Therefore, 13.524% of the variation in the observed y-values can be explained by the estimated regression equation.
Q8
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.
Ans:
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.
Q9
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.
Ans:
0.987
0.013
0.993
Q10
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
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.
Solution
Q1
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
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.
Q2
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.
Ans: 0.966……………….please follow the link below to purchase all the solutions at $5