Question:
The estimated regression equation is \(\hat{y}=60+5X\). What is the slope of this regression equation?
The estimated regression equation is \(\hat{y}=60+5X\). What is the slope of this regression equation?
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In the regression equation \(\hat{y}=a+bX\), the coefficient of \(X\) is the slope.
Updated On: May 22, 2026
- 12
- 60
- 5
- 300
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Verified By Collegedunia
The Correct Option is C
Solution and Explanation
Concept: A simple linear regression equation is generally written as:
\[
\hat{y}=a+bX
\]
where \(a\) is the intercept and \(b\) is the slope.
Step 1: Compare the given equation with standard form.
Given equation is: \[ \hat{y}=60+5X \] Standard form is: \[ \hat{y}=a+bX \]
Step 2: Identify intercept and slope.
Here, \[ a=60 \] and \[ b=5 \]
Step 3: Meaning of slope.
The slope tells how much \(\hat{y}\) changes when \(X\) increases by one unit. \[ \Delta \hat{y} = 5 \text{ when } \Delta X = 1 \] Therefore, the slope of the regression equation is \(5\).
Step 1: Compare the given equation with standard form.
Given equation is: \[ \hat{y}=60+5X \] Standard form is: \[ \hat{y}=a+bX \]
Step 2: Identify intercept and slope.
Here, \[ a=60 \] and \[ b=5 \]
Step 3: Meaning of slope.
The slope tells how much \(\hat{y}\) changes when \(X\) increases by one unit. \[ \Delta \hat{y} = 5 \text{ when } \Delta X = 1 \] Therefore, the slope of the regression equation is \(5\).
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