Find the equation of the least-squares line for the given data. Draw a scatter diagram for the given data and graph the least-squares line. x
1
2
3
4
5
6
Y
4)5
5
3
2
3)5
1

Please round the coefficients in your equation to two decimal places.

A)
B)
C)
D)

Question

Find the equation of the least-squares line for the given data. Draw a scatter diagram for the given data and graph the least-squares line. x
1
2
3
4
5
6
Y
4)5
5
3
2
3)5
1
​
Please round the coefficients in your equation to two decimal places.
​
A) ​ 
B) ​ 
C) ​ 
D) ​

Quizplus · Accepted Answer

Using the least-squares method, we can find the equation of the line:

Slope:

$$
m=\frac{\sum \left(x_i-\bar{x}\right)\left(y_i-\bar{y}\right)}{\sum \left(x_i-\bar{x}\right)^2}
$$

Substituting in the values we get:

$$
m=\frac{(1-3.5)(4.5-2)+(2-3.5)(5-2)+(3-3.5)(3-2)+(4-3.5)(2-2)+(5-3.5)(3.5-2)+(6-3.5)(1-2)}{(1-3.5)^2+(2-3.5)^2+(3-3.5)^2+(4-3.5)^2+(5-3.5)^2+(6-3.5)^2}
$$

Simplifying, we get:

$$
m=-\frac{9}{14}
$$

Y-Intercept:

$$
b=\bar{y}-m\bar{x}
$$

Substituting in the values we get:

$$
b=2.86\bar{6}
$$

Therefore, the equation of least-squares line is:

$$
y=-\frac{9}{14}x+2.86
$$

The scatter plot of the given data and the least-squares line is:

![scatterplot](https://i.imgur.com/Xn2GkfW.png)

The line in option B best represents the least-squares line that fits the given data.

Find the Equation of the Least-Squares Line for the Given