Math / Data & Statistics

QuestionGiven the equation of a regression line is $\hat{y}=-4.5 x+7.8$ , what is the best predicted value for $y$ given $x=4.0$ ? Assume that the variables x and y have a significant correlation. $-10.20$ 10.20 $-25.80$ 25.80

Studdy Solution

STEP 1

1. The regression equation is given as $\hat{y} = -4.5x + 7.8$ .
2. The correlation between $x$ and $y$ is significant, so the regression equation is a good predictor.
3. We need to find the predicted value of $y$ when $x = 4.0$ .

STEP 2

1. Substitute the given value of $x$ into the regression equation.
2. Calculate the predicted value of $y$ .

STEP 3

Substitute $x = 4.0$ into the regression equation:
$\hat{y} = -4.5(4.0) + 7.8$

STEP 4

Calculate the predicted value of $y$ :
$\hat{y} = -4.5 \times 4.0 + 7.8 = -18.0 + 7.8 = -10.2$
The best predicted value for $y$ when $x = 4.0$ is:
$\boxed{-10.20}$

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