x | y |
5 | 8 |
9 | 10 |
11 | 13 |
17 | 19 |
Use the Paired Data Set. Find the equation for the least-squares regression line
x y
5 8
9 10
11 13
17 19
Use the Paired Data Set.
Find the equation for the least-squares regression line
xyx⋅yx⋅x1584025291090813111314312141719323289sum4250596516
We find for the values:
N=4∑X=42∑Y=50∑XY=596∑X2=516
Slope(b)=N⋅∑XY−(∑X)⋅(∑Y)N⋅∑X2−(∑X)2=4⋅596−(42)⋅(50)4⋅516−(42)2=2384−21002064−1764=284300=0.94666666667
Intercept(a)=∑Y−b⋅(∑X)N=50−0.94666666667⋅(42)4=50−0.94666666667⋅(42)4=50−39.764=10.244=2.56
Regression Equation(y)=a+bxy=2.56+0.94¯6⋅x