this is the Estimated regression equation i produced: ŷ= 1.68 - 4.39 x
im not sure but i interpreted as it would indicate that for every hour spent studying per week, the students grade percentage increases by 4.39%.
so my question is i have to calculate the predicted grade for a student who studies 15 hours per week. Im confused because when I plug 15 for x, the students grade percentage is 64.17% and that seems too low for someone who studies 15 hours a week?
First of all I would question the validity of that equation.
Surely it would have to be something like ŷ= 1.68 + 4.39 x
The way you have it, would mean that the more he studied, the lower the grade !!
Secondly, I don't see how you got 64.17
If you used your equation it would be 1.68 - 4.39(15) = -64.17
Did you just ignore the negative?
Had you used the more probable ŷ= 1.68 + 4.39 x
you would get 1.68 + 4.39(15) = 67.53
Where did this equation come from ?
To calculate the predicted grade for a student who studies 15 hours per week using the estimated regression equation ŷ = 1.68 - 4.39x, you substitute the value of x (hours studied per week) into the equation.
If we plug x = 15 into the equation, we get:
ŷ = 1.68 - 4.39(15) = 1.68 - 65.85 = - 64.17
The negative value you obtained for ŷ indicates that the predicted grade is below zero. However, it's important to note that regression equations are statistical models that estimate average trends, and they may not always accurately predict individual data points.
In this case, it appears that the regression model does not accurately predict the grade for a student who studies 15 hours per week, as a grade below zero does not make sense.
It's possible that the model you have developed may not adequately capture the relationship between study hours and student grades. This could be due to various factors such as sample size, data quality, or the need for additional variables in the model.
To improve the accuracy of your predictions, you could consider refining your model by incorporating more data points or including other variables that may influence grades, such as prior knowledge, class difficulty, or study techniques.