Given below are seven observations collected in a regression study on two variables, x (independent variable) and y (dependent variable). Develop the least squares estimated regression equation. What is the coefficient of determination? x y 2 12 3 9 6 8 7 7 8 6 7 5 9 2

Step-by-step explanation:

Hello!

Given the independent variable X and the dependent variable Y (see data in attachment)

The regression equation is

^Y= b₀ + bX

Where

b₀= estimation of the y-intercept

b= estimation of the slope

The formulas to manually calculate both estimations are:

n=7

∑X= 42

∑X²= 292

∑Y= 49

∑Y²= 403

∑XY= 249

^Y= 13.75 - 1.13X

Using the raw data you can calculate the coefficient of determination as:

This means that 84% of the variability of the dependent variable Y is explained by the response variable X under the model ^Y= 13.75 - 1.13X

I hope this helps!