Math  /  Algebra

QuestionK This question: 1 point(s) possible Given that the equation of a regression line is ŷ = 3.5x-5.4, what is the best predicted value for y given that x = -1.22 Assume that the variables x and y have a significant correlation. O A. 12.3 OB. - 12.3 OC. -6.9 OD. - 9.6

Studdy Solution

STEP 1

1. The equation of the regression line is given by y^=3.5x5.4 \hat{y} = 3.5x - 5.4 .
2. We are tasked with finding the predicted value of y y when x=1.22 x = -1.22 .
3. The variables x x and y y have a significant correlation, so the regression line is a good predictor.

STEP 2

1. Substitute the given value of x x into the regression equation.
2. Calculate the predicted value y^ \hat{y} .
3. Compare the calculated value with the given options to determine the best predicted value.

STEP 3

Substitute x=1.22 x = -1.22 into the regression equation y^=3.5x5.4 \hat{y} = 3.5x - 5.4 :
y^=3.5(1.22)5.4 \hat{y} = 3.5(-1.22) - 5.4

STEP 4

Calculate y^ \hat{y} by performing the multiplication and subtraction:
y^=3.5×(1.22)5.4 \hat{y} = 3.5 \times (-1.22) - 5.4 y^=4.275.4 \hat{y} = -4.27 - 5.4 y^=9.67 \hat{y} = -9.67

STEP 5

Compare the calculated value y^=9.67 \hat{y} = -9.67 with the given options:
- Option A: 12.3 - Option B: -12.3 - Option C: -6.9 - Option D: -9.6
The closest value to our calculated result 9.67-9.67 is Option D: -9.6.
The best predicted value for y y given x=1.22 x = -1.22 is:
9.6 \boxed{-9.6}

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