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The equation of a regression line is \hat{y}=3.4x+4.2. What is the predicted value of \hat{y} for...

Question:

The equation of a regression line is {eq}\hat{y}=3.4x+4.2 {/eq}.

What is the predicted value of {eq}\hat{y} {/eq} for {eq}x = 11 {/eq}?

a) 33.2

b) -5.6

c) 41.6

d) cannot be calculated

e) None of these

Regression Line:

When we are determining a regression line to represent points in a scatter plot, the line being calculated will follow the same form as the equation of a line:

{eq}\bar{y} = a+ bx {/eq}

Every {eq}x {/eq}-value we substitute in this line will produce a {eq}y {/eq}-value that, when subtracted from the observed value, produces a residual.

Answer and Explanation:

The predicted value of {eq}\hat{y} {/eq} for {eq}x=11 {/eq} is the value of {eq}\hat{y}=3.4x+4.2 {/eq} when {eq}x=11 {/eq} is plugged in.

Let's plug in {eq}x=11 {/eq} into {eq}3.4x+4.2 {/eq}:

{eq}\begin{align*} \\ \displaystyle \hat{y}&=3.4x+4.2\\\\ &=3.4(11)+4.2\\\\ & = 41.6\\\\ \end{align*} {/eq}

Therefore, option {eq}c {/eq} is right.


Learn more about this topic:

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Simple Linear Regression: Definition, Formula & Examples

from

Chapter 8 / Lesson 2
65K

Simple linear regression is a great way to make observations and interpret data. In this lesson, you will learn to find the regression line of a set of data using a ruler and a graphing calculator.


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