Regression equations are used to represent the relationship between the x and y variables.
The regression equation is [tex]\mathbf{y =-0.39X +467.84}[/tex]
Using a graphing calculator, we have the following parameters
- Sum of x: [tex]\mathbf{\sum x = 269}[/tex]
- Sum of y: [tex]\mathbf{\sum y = 3170}[/tex]
- Mean of x: [tex]\mathbf{\bar x = 38.4286}[/tex]
- Mean of y: [tex]\mathbf{\bar y = 452.8571}[/tex]
- Sum of squares: [tex]\mathbf{SS_x = 1679.7143}[/tex]
- Sum of products: [tex]\mathbf{SP = -648.5714}[/tex]
The regression equation is represented as:
[tex]\mathbf{y =bX +a}[/tex]
Where:
[tex]\mathbf{b = \frac{SP}{SS_x}}[/tex] and [tex]\mathbf{a = \bar y-b \times \bar x}[/tex]
So, we have:
[tex]\mathbf{b = \frac{-648.5714}{1679.7143}}[/tex]
[tex]\mathbf{b = -0.39}[/tex]
Also, we have:
[tex]\mathbf{a = \bar y-b \times \bar x}[/tex]
This gives:
[tex]\mathbf{a = 452.8571 - (-0.39 \times 38.4286) }[/tex]
[tex]\mathbf{a = 467.84}[/tex]
Substitute values for (b) and (a) in [tex]\mathbf{y =bX +a}[/tex]
[tex]\mathbf{y =-0.39X +467.84}[/tex]
Hence, the regression equation is [tex]\mathbf{y =-0.39X +467.84}[/tex]
See attachment for the scatter plot
Read more about regression equations at:
https://brainly.com/question/7656407
