The table below shows the amount of time each of the 15 students in an introductory chemistry class spent studying for the first exam, and the student's score on the exam out of 100.
x (minutes spent studying) y (score on exam in points)
60 67
50 60
45 72
100 76
80 74
70 87
90 88
0 65
70 84
100 83
120 71
60 74
150 95
120 82
0 74
To check this is entered correctly on your calculator, press [stat], go to CALC, and select "2:2-Var Stats". Run this on your two lists. When you scroll down the list, you should see Σxy=89020
Enter the data into your calculator and obtain a linear equation of best fit using the linear regression feature. Type the equation here, in the form y=mx+b
. If necessary, round the values of m
and b
to three decimal places.
Based on your regression equation, what score would you predict for a student who has studied for 1 hour and 30 minutes? Round your answer to a whole number of points.
points
Based on your regression equation, how much time should a "typical" student spend studying if they wanted to score at least 90 points on the exam? Round your answer up to the next full minute.
minutes
The linear regression equation of best fit obtained is:
y = 0.759x + 60.214
Therefore, the predicted score for a student who has studied for 1 hour and 30 minutes (90 minutes) is:
y = 0.759(90) + 60.214
y = 68.571 + 60.214
y = 128.785
Rounded to a whole number, the predicted score is 129 points.
To score at least 90 points on the exam, a "typical" student should spend:
y = 90
90 = 0.759x + 60.214
29.786 = 0.759x
x ≈ 39.266
Rounded up to the next full minute, a "typical" student should spend 40 minutes studying.