Which model do you believe would be the better model to use? Please write the best simple linear equation below and explain why it is the ‘best’ of the three options above. Interpret the value of the estimate of βo in the model you selected above. Interpret the value of the estimate of β1 in the model you selected above.
The administrator of a school board in a large county was analyzing the average mathematics test scores in the schools under her control. She noticed that there were dramatic differences in scores among the schools. In an attempt to improve the scores of all the schools, she isolated factors that could account for the differences and were easily obtained from HR. Accordingly, she took a random sample of 40 schools across the county and for each determined:
Test Score, Y: the
Math Dgr, X1: the percentage of teachers in each school who have at least one university degree in math
Age, X2: the mean age of the math teachers at the school sampled
Income, X3: the mean annual income of the math teachers at the school sampled
Conduct a simple linear
Variable Equation S
Math Dgr 50.651+0.2634X 8.084
Age 47.305+0.3786X 8.8429
Income 51.27+0.2925X 8.9083
- Which model do you believe would be the better model to use? Please write the best simple linear equation below and explain why it is the ‘best’ of the three options above.
- Interpret the value of the estimate of βo in the model you selected above.
- Interpret the value of the estimate of β1 in the model you selected above.
Data:
| Test Score | Math Dgr | Age | Income |
| 73.9 | 77 | 52 | 44.4 |
| 59.4 | 48 | 32 | 49 |
| 64.6 | 33 | 50 | 52.6 |
| 59.8 | 25 | 43 | 39.6 |
| 58.8 | 25 | 40 | 40.7 |
| 58.7 | 39 | 33 | 38 |
| 68.5 | 71 | 37 | 25.1 |
| 54.7 | 24 | 48 | 46.5 |
| 61.7 | 25 | 47 | 38.4 |
| 81.6 | 49 | 50 | 44.6 |
| 83.7 | 56 | 59 | 54.8 |
| 62.5 | 46 | 40 | 38.5 |
| 68.2 | 75 | 41 | 44.8 |
| 51.1 | 25 | 51 | 39.9 |
| 44 | 46 | 38 | 55.6 |
| 65.7 | 68 | 45 | 44.1 |
| 69.6 | 27 | 49 | 47.5 |
| 54.5 | 23 | 31 | 40 |
| 56.5 | 48 | 38 | 40.2 |
| 44.8 | 41 | 38 | 28.3 |
| 72.6 | 79 | 39 | 44.8 |
| 65.3 | 76 | 43 | 34.5 |
| 64.9 | 31 | 39 | 28 |
| 69.8 | 63 | 49 | 51.4 |
| 75.3 | 72 | 49 | 55.2 |
| 57 | 30 | 23 | 24.6 |
| 52.8 | 62 | 34 | 29.7 |
| 71.3 | 75 | 36 | 32.1 |
| 55.2 | 43 | 35 | 32.6 |
| 62.6 | 64 | 50 | 37.4 |
| 58.2 | 44 | 45 | 42.9 |
| 71.8 | 46 | 29 | 34.4 |
| 69.9 | 35 | 39 | 45.6 |
| 70.1 | 63 | 34 | 52.9 |
| 66.1 | 56 | 36 | 22.1 |
| 71.7 | 57 | 59 | 55.1 |
| 68.8 | 41 | 40 | 33.7 |
| 45 | 27 | 40 | 19.8 |
| 61.9 | 37 | 44 | 48.2 |
| 56 | 36 | 56 | 55.9 |
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