Regression Analysis: Estimating the Value of Y for X = 5 | CFA® Level 1 Test Prep

Estimating the Value of Y for X = 5

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Question

The results of the regressions using 200 observation on a variable Y against X are as follows:

Coefficient Standard error -

intercept 3.62.1

slope 8.11.3

R square = 49%

If an observation on X indicates X = 5 the estimated value of Y would be ________.

Answers

Explanations

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A. B. C. D.

A

From the information given, the regression equation is Y = 3.6 + 8.1X + error term. The expected value of the error is zero. Hence, when X = 5, the estimated value of Y equals 3.6 + 8.1*5 = 44.1.

To estimate the value of Y when X equals 5, we can use the regression equation:

Y = Intercept + Slope * X

Given the coefficients from the regression results:

Intercept = 3.6 Slope = 8.1

Substituting these values into the equation, we get:

Y = 3.6 + 8.1 * X

Plugging in X = 5:

Y = 3.6 + 8.1 * 5 Y = 3.6 + 40.5 Y = 44.1

Therefore, the estimated value of Y when X = 5 is 44.1.

The correct answer is A. 44.1.