Math / Data & Statistics

QuestionFind the best predicted value of $y$ given that $x=5$ for 6 pairs of data that yield $r=0.444, \bar{y}=18.3$ and the regression equation $y=2+5 x$ . State the critical level.

Studdy Solution

STEP 1

1. The regression equation is given as $y = 2 + 5x$ .
2. The correlation coefficient $r = 0.444$ .
3. The mean of $y$ is $\bar{y} = 18.3$ .
4. We are asked to find the predicted value of $y$ when $x = 5$ .

STEP 2

1. Use the regression equation to calculate the predicted value of $y$ for $x = 5$ .
2. State the critical level based on the correlation coefficient.

STEP 3

Substitute $x = 5$ into the regression equation $y = 2 + 5x$ :
$y = 2 + 5(5)$
$y = 2 + 25$
$y = 27$

STEP 4

The critical level is typically determined by the correlation coefficient $r$ . A correlation coefficient $r = 0.444$ indicates a moderate positive relationship between $x$ and $y$ .
The best predicted value of $y$ when $x = 5$ is:
$\boxed{27}$
The critical level indicates a moderate positive correlation.

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