Question

A regression was run to determine if there is a relationship between hours of study per week (x) and the final exam scores (y). The results of the regression were:

y=ax+b
a=6.578
b=20.35
r²=0.3721
r=0.61
Use this to predict the final exam score of a student who studies 7 hours per week, and please round your answer to a whole number.

Answer 1

To predict the final exam score for a student who studies 7 hours per week, we calculate y = 6.578(7) + 20.35, which equals 66.396 and is rounded to 66. The regression equation and coefficients of determination are key components in regression analysis.

Step-by-step explanation:

To predict the final exam score of a student who studies 7 hours per week using the regression equation, we simply plug the value of x (hours of study) into the equation y = ax + b. With a slope (a) of 6.578 and a y-intercept (b) of 20.35, the equation given is y = 6.578x + 20.35. So, if a student studies for 7 hours, the predicted score (y) would be:

y = 6.578(7) + 20.35

Calculating this, we get:

y = 46.046 + 20.35

y = 66.396

After rounding to the nearest whole number, the predicted final exam score would be 66.

The regression equation, correlation coefficient (r), and the coefficient of determination (r²) are all key elements in regression analysis. The regression equation is used to predict the value of the dependent variable based on the independent variable. Here, the coefficient of determination, r² = 0.3721, tells us that approximately 37.21% of the variance in final exam scores can be explained by the number of study hours per week.