A Multiple Regression Analysis Produced the Following Output from Minitab

question 8

Multiple Choice

A multiple regression analysis produced the following output from Minitab. Regression Analysis: Y versus x₁ and x₂
Predictor Coef SE Coef T P
Constant -0.0626 0.2034 -0.31 0.762
X₁ 1.1003 0.5441 2.02 0.058
X₂ -0.8960 0.5548 -1.61 0.124
S = 0.179449 R-Sq = 89.0% R-Sq(adj) = 87.8%
Analysis of Variance
Source DF SS MS F P
Regression 2 4.7013 2.3506 73.00 0.000
Residual Error 18 0.5796 0.0322
Total 20 5.2809
The overall proportion of variation of y accounted by x₁ and x₂ is _______

• A)0.179
• B)0.89
• C)0.878
• D)0.203
• E)0.5441

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Definitions:

Coefficient of Determination

A statistical measure, often denoted as R^2, that represents the proportion of the variance for a dependent variable that's explained by one or more independent variables in a regression model.

Slope

The rate of change in the dependent variable for a unit change in the independent variable in a linear relationship.

Regression Line

A line of best fit through a scatterplot of data points in regression analysis, showing the relationship between the independent and dependent variables.

Positive

A term often used in statistics to denote a value or outcome that is above zero or indicates the presence of a condition or characteristic.