Last summer, five randomly selected students took a math aptitude test before they began their statistics course in the fall. The data on (i) math aptitude test scores and (ii) performance on statistics course are given below: Student 1 2 3 4 5Math aptitude test score 95 85 80 70 60Statistic Grade 85 95 70 65 70a. What regression equation best predicts statistics performance, based on math aptitude scores? b. What significance is there to a ? Explain briefly. What significance is there to b ? Explain briefly. c. If a student scored an 80 on the aptitude test, what would be the estimated statistics grade? d. Determine the standard error of the estimate? What does it indicate? e. Calculate and interpret the coefficient of correlation and the coefficient of determination.

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19-12-2022
Mathematics

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Last summer, five randomly selected students took a math aptitude test before they began their statistics course in the fall. The data on (i) math aptitude test scores and (ii) performance on statistics course are given below: Student 1 2 3 4 5Math aptitude test score 95 85 80 70 60Statistic Grade 85 95 70 65 70a. What regression equation best predicts statistics performance, based on math aptitude scores? b. What significance is there to a ? Explain briefly. What significance is there to b ? Explain briefly. c. If a student scored an 80 on the aptitude test, what would be the estimated statistics grade? d. Determine the standard error of the estimate? What does it indicate? e. Calculate and interpret the coefficient of correlation and the coefficient of determination.

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kumarravichandra kumarravichandra · Answer 1 · 2022-12-21T23:34:56-05:00

The regression equation y=0.37x+62.5 predicts statistics performance based on math aptitude scores, with a strong positive correlation and 65.1% of the variation explained.

a. The regression equation that best predicts statistics performance, based on math aptitude scores is y = 0.37x + 62.5, where y is the statistics grade and x is the math aptitude test score.

b. The significance of a is the intercept of the regression line, which is the predicted value of the statistics grade when the math aptitude score is 0. The significance of b is the slope of the regression line, which indicates the amount of change in the statistics grade for a unit change in the math aptitude score.

c. If a student scored an 80 on the aptitude test, the estimated statistics grade would be 79.5.

d. The standard error of the estimate is 6.36. This indicates the average amount of error between the observed values and the predicted values.

e. The coefficient of correlation is 0.807 and the coefficient of determination is 0.651. The coefficient of correlation indicates a strong positive linear relationship between the math aptitude scores and statistics grades. The coefficient of determination indicates that 65.1% of the variation in statistics grades is explained by the math aptitude scores.

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