# Fitting a straigjt line to a set of data yields the following prediction line. Complete c below. ...

## Question:

Fitting a straigjt line to a set of data yields the following prediction line. Complete c below.

{eq}\widehat{Y}_{i} = 2+9x_{i} {/eq}

c. Predict the mean value of Y for X = 4.

{eq}\widehat{Y}= {/eq} _ (Simplify your answer)

## Predicted value

Predicted value is the predicted output from a linear regression equation. The equation has the form y =a+bx where b is the slope and a is the intercept. It is used to find the difference between predicted data and observed data.

## Answer and Explanation: 1

We are given that

{eq}\hat{Y}_{i} = 2 + 9 X_{i} {/eq}

Substituting {eq}X_{i} {/eq} = 4, the predicted mean value for Y is

{eq}\hat{Y}_{i} {/eq} = 2 + 9 (4)

{eq}\hat{Y}_{i} {/eq} =2 + 36

{eq}\hat{Y}_{i} {/eq} = 38

#### Learn more about this topic: Predictor Variable: Definition & Example

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Chapter 9 / Lesson 15
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Did you know predictor variables are commonly used in nonexperimental research designs? Learn more about predictor variables from examples, and then test your knowledge with a quiz.