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you're interested in predicting college grades (y) from sat scores (x). you know that the mean of the sat scores is 485 with a standard deviation of 85. the average college gpa is 3.1 within a standard deviation of 0.4. the correlation between sat scores and college grades is 0.71. what is the equation of the regression of grades (y) on scores (x)?

Respuesta :

The equation of the regression of grades on scores is y = 0.003x + 1.645

The mean of the sat scores = 485

The standard deviation = 85

The average college gpa = 3.1

The standard deviation = 0.4

The correlation between sat scores and college grades = 0.71

The regression equation is

y = mx + b

The value of m = (0.71) × (0.4/85)

= 0.003

Substitute the values in the regression equation and find the value of b

3.1 = 0.003×485 + b

3.1 = 1.455 + b

b = 3.1 - 1.455

b = 1.645

The equation is

y = 0.003x + 1.645

Therefore, the regression equation is y = 0.003x + 1.645

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