Question

(b) the data seems to have a linear trend. so, keith wants to find a linear equation that could approximately model the data. select \compute\ to generate the values used for a linear regression model. write the values in your answer to 3 decimal places.

x | 1 | 3 | 4 | 5 | 6 | 7 | 9
---|---|---|---|---|---|---|---
y | 7 | 5 | 6 | 5 | 4 | 3 | 2

compute

lin reg: y = ax + b

a ≈ -0.619
b ≈ 7.067
r² ≈ 0.909
r ≈ -0.953

the linear equation that best fits the data is y =

(c) use the equation from part (b) to help keith predict the value of y when x = 8. write your answer to 3 decimal places.

y =

Explanation:

Part (b)

Step1: Identify linear regression form

The linear regression model is given by \( y = ax + b \), where \( a \) is the slope and \( b \) is the y - intercept. From the given data, \( a=- 0.619\) and \(b = 7.067\).

Step2: Write the linear equation

Substitute the values of \( a \) and \( b \) into the equation \( y=ax + b \). So the equation is \( y=-0.619x + 7.067\).

Step1: Use the linear equation

We have the linear equation \( y=-0.619x + 7.067\) from part (b). We need to find the value of \( y \) when \( x = 8\).

Step2: Substitute \( x = 8\) into the equation

Substitute \( x = 8\) into \( y=-0.619x+7.067\). So \( y=-0.619\times8 + 7.067\). First, calculate \(-0.619\times8=-4.952\). Then, \( y=-4.952 + 7.067=2.115\).

Answer:

\(y=-0.619x + 7.067\)

Part (c)