Find the linear regression equation to represent the set of data belowRound all numbers to the nearest tenth Homework Grade (x) Test Grade (y) 7977 87 83 69 58 7060 5440 59 56 84 73 Using the regression equation, what would a student expect to get on the test if they scored a 34 on the homework?
First, calculate the mean of both sets of data:
Mean of Homework Grades (x): (79 + 77 + 83 + 69 + 58 + 70 + 60 + 54 + 40 + 59 + 56 + 84 + 73) / 13 = 66.4
Mean of Test Grades (y): (87 + 83 + 69 + 58 + 70 + 60 + 54 + 40 + 59 + 56 + 84 + 73) / 13 = 67.7
Next, calculate the values needed for the linear regression equation:
x*x = 61799
y*y = 46039
x*y = 48193
x*x = 9175
Calculate the slope (m):
m = (13 * 48193 - 79 * 77) / (13 * 61799 - 79 * 79)
m = (626309 - 6083) / (803187 - 6241)
m = 620226 / 797946
m = 0.777
Calculate the y-intercept (b):
b = (67.7) - (0.777 * 66.4)
b = 67.7 - 51.6
b = 16.1
So, the linear regression equation is:
y = 0.8x + 16.1
To find what a student with a homework grade of 34 would score on the test:
y = 0.8 * 34 + 16.1
y = 27.2 + 16.1
y = 43.3
Therefore, a student who scored a 34 on the homework would be expected to score a 43.3 on the test based on the linear regression equation.