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c. 1: What are the numerical value and physical units of the s variable in the r

ID: 3301691 • Letter: C

Question

c. 1: What are the numerical value and physical units of the s variable in the regression analysis output? c.2: Interpret the meaning of s. c.3: Explain why the s variable is important c.4: What are the value and physical units of the slope parameter 1hat? c.5: Provide a complete interpretation of the slope parameter.

Child Midparent
61.7 70.5
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Explanation / Answer

We are given data of child and midparent.

Dependent variable : Midparent

Independent variable : Child

Here we have to fit regression of midparent on child.

We can fit regression in MINITAB.

steps :

ENTER data into MINITAB sheet --> STAT --> Regression --> Regression --> Response : Midparent --> Predictors : Child--> Results : select second option --> ok --> ok

Regression Analysis: midparent versus Child


The regression equation is
midparent = 46.1 + 0.326 Child

Predictor Coef SE Coef T P
Constant 46.135 1.412 32.67 0.000
Child 0.32565 0.02073 15.71 0.000

S = 1.589 R-Sq = 21.0% R-Sq(adj) = 21.0%

Analysis of Variance

Source DF SS MS F P
Regression 1 623.26 623.26 246.84 0.000
Residual Error 926 2338.10 2.52
Total 927 2961.36

c.1: What are the numerical value and physical units of the s variable in the regression analysis output?

S is known both as the standard error of the regression and as the standard error of the estimate.

S represents the average distance that the observed values fall from the regression line. Conveniently, it tells you how wrong the regression model is on average using the units of the response variable. Smaller values are better because it indicates that the observations are closer to the fitted line.

c.2: Interpret the meaning of s.

S is 1.589, which tells us that the average distance of the data points from the fitted line is about 1.589% Midparent.

c.3: Explain why the s variable is important

In many cases, I prefer the standard error of the regression over R-squared. I love the practical, intuitiveness of using the natural units of the response variable. And, if I need precise predictions, I can quickly check S to assess the precision.

Conversely, the unit-less R-squared doesn’t provide an intuitive feel for how close the predicted values are to the observed values. Further, as I detailed here, R-squared is relevant mainly when you need precise predictions. However, you can’t use R-squared to assess the precision, which ultimately leaves it unhelpful.

c.4: What are the value and physical units of the slope parameter 1hat? c.5: Provide a complete interpretation of the slope parameter

Slope = coefficient of Child in regression equation = 0.326

Interpretation : For one unit change in Child will be 0.326 unit increase in Midparent.

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