Question

Use the given data to find the best predicted value of the response variable. Ten pairs of data yield requals0.003 and the regression equation ModifyingAbove y with caret equals2plus3x. ​Also, y overbarequals5.0. What is the best predicted value of y for xequals​2?

Answer 1

Answer:

$\hat y=3(2) +2=8$

Step-by-step explanation:

Data given

r=0.003 represent the correlation coefficient

$bar y =5$ represent the sample mean for the y observations

Solution to the problem

We assume that they use least squares in order to find the best regression model. The slope is given by the following formula:

$m=\frac{S_{xy}}{S_{xx}}$

Where:

$S_{xy}=\sum_{i=1}^n x_i y_i -\frac{(\sum_{i=1}^n x_i)(\sum_{i=1}^n y_i)}{n}$

$S_{xx}=\sum_{i=1}^n x^2_i -\frac{(\sum_{i=1}^n x_i)^2}{n}$

And the slope on this case is:

$m=3$

Nowe we can find the means for x and y like this:

$\bar x= \frac{\sum x_i}{n}=5$

$\bar y= \frac{\sum y_i}{n}$

And we can find the intercept using this:

$b=\bar y -m \bar x=5-(3*\bar x)=2$

So the line would be given by:

$\hat y=3x +2$

And the best predicted value for x=2 would be:

$\hat y=3(2) +2=8$