Given the following computer regression output, write the linear regression equation.
[tex]
\begin{array}{c}
\begin{array}{cccc}
\text { Predictor } & \text { Coef } & \text { SE Coef } & T \
\text { Constant } & -169.65 & 56.67 & -2.99 \
X & 4.58 & 0.79 & 5.84 \
s=17.72 & r-sq=85.0 \% & R-sq(adj)=82.5 \%
\end{array} \
\hat{y}=[?]+\square x
\end{array}
[/tex]
Answer (1)
Identify the constant term (y-intercept) from the regression output: -169.65.
Identify the coefficient of the predictor variable X from the regression output: 4.58.
Substitute the values into the linear regression equation: y ^ = Constant + Coefficient of X ∗ x .
Write the final equation: y ^ = − 169.65 + 4.58 x
Explanation
Identifying Coefficients The regression output provides us with the coefficients needed to form the linear regression equation. We need to identify the constant term (y-intercept) and the coefficient for the predictor variable X.
Extracting Values From the regression output, we can see that the constant term is -169.65 and the coefficient for X is 4.58.
Forming the Equation Now, we substitute these values into the linear regression equation: y ^ = Constant + Coefficient of X ∗ x y ^ = − 169.65 + 4.58 x
Final Equation Therefore, the linear regression equation is y ^ = − 169.65 + 4.58 x .
Examples
Linear regression equations are used in various fields. For example, a store owner might use a regression equation to predict daily sales based on the amount spent on advertising. If the equation is y ^ = 50 + 10 x , where y ^ is the predicted daily sales and x is the amount spent on advertising (in dollars), it suggests that with no advertising, the store makes $50 in sales, and for every dollar spent on advertising, the sales increase by $10. This helps in making informed decisions about advertising budgets.
