Answer:
Kindly check explanation
Step-by-step explanation:
Given the data:
ACT (X) :
21
24
26
27
29
25
25
30
GPA (Y) :
2.8
3.4
3.0
3.5
3.6
3.0
2.7
3.7
Relationship between GPA and ACT using a linear regression calculator :
ŷ = 0.1022X + 0.56813
Slope = 0.1022
Intercept = 0.56813
The relationship between GPA and ACT is in the positive direction, this can be inferred from the slope value which is positive
The intercept value ; 0.56813 means with a GPA score of 0 ; predicted ACT score will be 0.56813
Explain. How much higher is the GPA predicted to be if the ACT score increases by 5 points?
If ACT score increases by 5 ; predicted GPA will be:
Increase = 0.1022(5)
ACT score will increases by 0.511
ii) Compute the fitted values and the residuals for each observation and verify that the residuals sum to zero.
y = 0.1022(21) + 0.56813 = 2.71433
y = 0.1022(24) + 0.56813 = 3.02093
y = 0.1022(26) + 0.56813 = 3.22533
y = 0.1022(27) + 0.56813 = 3.32753
y = 0.1022(29) + 0.56813 = 3.53193
y = 0.1022(25) + 0.56813 = 3.12313
y = 0.1022(25) + 0.56813 = 3.12313
y = 0.1022(30) + 0.56813 = 3.63413
Residual:
2.8 - 2.71433 = 0.08567
3.4 - 3.02093 = 0.37907
3.0 - 3.22533 = −0.22533
3.5 - 3.32753 = 0.17247
3.6 - 3.53193 = 0.06807
3.0 - 3.12313 = −0.12313
2.7 -3.12313 = −0.42313
3.7 - 3.63413 = 0.06587
0.08567+0.37907−0.22533+0.17247+0.06807−0.12313−0.42313+0.06587 = −0.00044 = 0.00
iii) What is the predicted value of GPA when ACT = 20?
ŷ = 0.1022(20) + 0.56813
= 2.61
