Below is given a partial Minitab output based on a sample of 25 observations.

Coefficient

Standard Error

Constant
145.321

48.682

X1
25.625

9.150

X2
-5.720

3.575

X3
0.823

0.183

The estimated regression equation is

Question

Below is given a partial Minitab output based on a sample of 25 observations.

Coefficient
	
Standard Error

Constant	
145.321
	
48.682

X1	
25.625
	
9.150

X2	
-5.720
	
3.575

X3	
0.823
	
0.183

The estimated regression equation is

BlackTom AI · Accepted Answer

The problem presents a partial Minitab output for a multiple regression and asks for the estimated regression equation.
First, I restate what the table provides: the intercept (Constant) is 145.321 with a standard error of 48.682, and the coefficients for the predictors are X1 = 25.625, X2 = -5.720, and X3 = 0.823, each with their respective standard errors. The standard practice in linear regression is to write the estimated regression equation as Ŷ = β0 + β1X1 + β2X2 + β3X3, where β0 is the intercept and βi are the slopes associated with each predictor.
Option 1: If the first option is an empty string, it does not present any usable form of the equation. It fails to specify the intercept or any predictor terms, so it cannot be the regression equation implied by the output.
Option 2: If the second option is also an empty string, it is similarly deficient for the same reason: there is no β0 or predictor terms shown, so it does not reflect the given coefficients.
Option 3: A blank option again provides no model specification, making it invalid as a representation of the regression equation from the output.
Option 4: The fourth option being empty, like the others, fails to present a usable equation. In multiple-choice contexts, blank choices cannot correctly state the model.
Given the information in the table, the equation that aligns with all four coefficients is the one that uses the intercept 145.321 and the predictor coefficients 25.625 for X1, -5.720 for X2, and 0.823 for X3. These values come directly from the Constant row and each X1, X2, and X3 row in the output, forming the standard linear regression equation Ŷ = 145.321 + 25.625X1 - 5.720X2 + 0.823X3. The remaining blank options fail to encode any of these coefficients, so they do not represent the estimated model.
In short, the only viable form uses the intercept and the listed coefficients exactly as shown in the table, and it is constructed in the conventional Ŷ = β0 + β1X1 + β2X2 + β3X3 format with the corresponding numeric values.

Below is given a partial Minitab output based on a sample of 25 observations. Coefficient Standard Error Constant 145.321 48.682 X1 25.625 9.150 X2 -5.720 3.575 X3 0.823 0.183 The estimated regression equation is

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