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ACT SCORES: {23, 28, 22, 20, 23, 19, 20, 29, 27, 18} In addition to ACT...

ACT SCORES: {23, 28, 22, 20, 23, 19, 20, 29, 27, 18}

In addition to ACT scores of the students, consider the following set of data representing the GPAs of each student respectively.

{1.83, 4, 3.05, 3.77, 3.55, 2.58, 3.16, 3.39, 3.86, 2.92}
(a) Compute the correlation coefficient. What do you think about the relationship?

(b) Determine the equation of the least squares line by calculating the slope (b1) and intercept (b0). Use this equation to forecast the ACT score of a student with GPA 3.00.

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ACT Scores GPA 1.83 4.00 3.05 3.77 3.55 2.58 3.16 3.39 3.86 2.92 42.09 112.00 67.10 75.40 81.65 49.02 63.20 98.31 104.22 52.56 3.3489 16.0000 9.3025 14.2129 12.6025 6.6564 9.9856 11.4921 14.8996 8.5264 529 784 484 400 529 361 400 841 729 324 ΣΥ2-6381 23 28 20 23 19 20 29 27 18 ΣΧ-32-11 | ΣΥ-2291 ΣΧ*Y-745.55 | ΣΧ = 1070269| (a) Compute the correlation coefficient. What do you think about the relationship? Correlation coefficient can be determined by the following expression. 10 745.55-32.11 229 10(107.0269)-(32.11 10(5381) (220) 0.44154984 r-0.44155 We know that value of correlation coefficient(r) varies from -1 to 1 In this problem, value of 0.44154984 indicates a weak to moderate positive linear relationship between X and Y. Clearly a value less than 0.5, does not indicate a strong positive linear relationship between ACT Score and GPA (b) Determine the equation of the least squares line by calculating the slope (b1) and intercept (bo). Use this equation to forecast the ACT score of a student with GPA 3.00. Slope of the best fitting regression line bl - Slope of the best fiting regresion line-XYXY X2-nX

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