Complete the following worksheet and then use it to calculate the coefficient of determination. (9₁ - y)² (Yi - y)² 8.618 12.721 20.854 6.588 9.404 16.538 6.588 0.004 2.054 5.921 0.871 11.788 5.921 24.338 29.521 0.321 Ti Yi ŷ 50 20 19.369 50 21 19.369 3 55 19 18.409 4 55 19.5 18.409 5 60 20.5 17.449 6 60 19 17.449 7 65 16.5 16.489 8 65 15 16.489 9 70 14 15.529 10 70 15.5 15.529 11 80 13 13.609 12 80 14 13.609 13 90 11.5 11.689 14 90 11 11.689 15 40 17 21.289 Total i 1 2 8.618 3.903 3.903 1.032 1.032 0.003 0.003 0.818 0.818 7.977 7.977 22.509 22.509 23.577 113.297 The coefficient of determination (2) is 153.432

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**Calculating the Coefficient of Determination**

Complete the following worksheet and then use it to calculate the coefficient of determination.

| i  | \( x_i \) | \( y_i \) | \( \hat{y} \) | \( (\hat{y} - \bar{y})^2 \) | \( (y_i - \bar{y})^2 \) |
|----|-----------|-----------|--------------|-----------------------------|-------------------------|
| 1  | 50        | 20        | 19.369       | 8.618                       | 12.721                  |
| 2  | 50        | 21        | 19.369       | 8.618                       | 20.854                  |
| 3  | 55        | 19        | 18.409       | 3.903                       | 6.588                   |
| 4  | 55        | 19.5      | 18.409       | 3.903                       | 9.404                   |
| 5  | 60        | 20.5      | 17.449       | 1.032                       | 16.538                  |
| 6  | 60        | 19        | 17.449       | 1.032                       | 6.588                   |
| 7  | 65        | 16.5      | 16.489       | 0.003                       | 0.004                   |
| 8  | 65        | 15        | 16.489       | 0.003                       | 2.054                   |
| 9  | 70        | 14        | 15.529       | 0.818                       | 5.921                   |
| 10 | 70        | 15.5      | 15.529       | 0.818                       | 0.871                   |
| 11 | 80        | 13        | 13.609       | 7.977                       | 11.788                  |
| 12 | 80        | 14        | 13.609       | 7.977                       | 5.921                   |
| 13 | 90        | 11.5      | 11.689       | 22.509                      |
Transcribed Image Text:**Calculating the Coefficient of Determination** Complete the following worksheet and then use it to calculate the coefficient of determination. | i | \( x_i \) | \( y_i \) | \( \hat{y} \) | \( (\hat{y} - \bar{y})^2 \) | \( (y_i - \bar{y})^2 \) | |----|-----------|-----------|--------------|-----------------------------|-------------------------| | 1 | 50 | 20 | 19.369 | 8.618 | 12.721 | | 2 | 50 | 21 | 19.369 | 8.618 | 20.854 | | 3 | 55 | 19 | 18.409 | 3.903 | 6.588 | | 4 | 55 | 19.5 | 18.409 | 3.903 | 9.404 | | 5 | 60 | 20.5 | 17.449 | 1.032 | 16.538 | | 6 | 60 | 19 | 17.449 | 1.032 | 6.588 | | 7 | 65 | 16.5 | 16.489 | 0.003 | 0.004 | | 8 | 65 | 15 | 16.489 | 0.003 | 2.054 | | 9 | 70 | 14 | 15.529 | 0.818 | 5.921 | | 10 | 70 | 15.5 | 15.529 | 0.818 | 0.871 | | 11 | 80 | 13 | 13.609 | 7.977 | 11.788 | | 12 | 80 | 14 | 13.609 | 7.977 | 5.921 | | 13 | 90 | 11.5 | 11.689 | 22.509 |
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