(a) The scatterplot is:
(b) r = 0.952
(c) Yes, there is a positive linear relationship between the variables.
(d) The regression line is:
y = 0.131 x - 0.174
The calculations are:
ACT Score | College GPA | (x - xbar) | (y - ybar) | (x - xbar)*(y - ybar) | (x - xbar)² | (y - ybar)² |
16 | 1.85 | -8.9 | -1.243 | 11.0627 | 79.21 | 1.545049 |
18 | 2.2 | -6.9 | -0.893 | 6.1617 | 47.61 | 0.797449 |
24 | 2.8 | -0.9 | -0.293 | 0.2637 | 0.81 | 0.085849 |
25 | 3.5 | 0.1 | 0.407 | 0.0407 | 0.01 | 0.165649 |
34 | 4 | 9.1 | 0.907 | 8.2537 | 82.81 | 0.822649 |
27 | 3.18 | 2.1 | 0.087 | 0.1827 | 4.41 | 0.007569 |
29 | 3.9 | 4.1 | 0.807 | 3.3087 | 16.81 | 0.651249 |
25 | 2.9 | 0.1 | -0.193 | -0.0193 | 0.01 | 0.037249 |
30 | 4 | 5.1 | 0.907 | 4.6257 | 26.01 | 0.822649 |
21 | 2.6 | -3.9 | -0.493 | 1.9227 | 15.21 | 0.243049 |
xbar | ybar | Σ(x - xbar) | Σ(y - ybar) | Σ(x - xbar)*(y - ybar) | Σ(x - xbar)² | Σ(y - ybar)² |
24.9 | 3.093 | 0 | 0 | 35.803 | 272.9 | 5.17841 |
r = Σ(x - xbar)*(y - ybar)/√Σ(x - xbar)²*Σ(y - ybar)² | 0.9524 | |||||
b1 = Σ(x - xbar)*(y - ybar)/Σ(x - xbar)² | 0.131195 | |||||
bo = ybar - b1*xbar | -0.17374 |
6. I've been doing research on the leaders of our country, and found the educational records...