Linear model

S

Sue0113

Junior Member
Joined
Feb 1, 2012
Messages
114
Can anyone help with explaining a linear model and how I figure out if appropiate? Using Minitab, I have comeleted the graph model just need help at interpeting it.

This is the information supplied and the questions. I'm not understanding this chapter and wondering if someone can help me
Do you think a linear model is appropriate?
Interpret the slope of your model
Is your model likely to make reliable estimates?
What is the residual for a person who weighs 190 pounds and is 21% bodyfat?

Regression Analysis: Body Fat % versusWeight (lb)

The regression equation is
Body Fat % = - 27.38 + 0.2499 Weight (lb)


S = 7.04913 R-Sq = 48.5% R-Sq(adj) = 45.7%


Analysis of Variance

Source DF SS MS F P
Regression 1 843.33 843.325 16.97 0.001

Data

Waist (in) Weight (lb) Body Fat %
32 175 6
36 181 21
38 200 15
33 159 6
39 196 22
40 192 31
41 205 32
35 173 21
38 187 25
38 188 30
33 188 10
40 240 20
36 175 22
32 168 9
44 246 38
33 160 10
41 215 27
34 159 12
34 146 10
44 219 28
 
Last edited:
Sue0113 said:
Can anyone help with explaining a linear model and how I figure out if appropiate? Using Minitab, I have comeleted the graph model just need help at interpeting it.
Click to expand...
A "linear model" means that you use a straight line function as an approximation to the data. The best way to decide that is appropriate is to look at a scatter plot of the data - in this case Weight is the independent variable (plotted in the horizontal direction. ) and Body-Fat % is the dependent variable (plotted in the vertical direction). What does your eye tell you? If you laid a ruler down on the plot and tried to adjust it, would you get a fair representation of the data?

If your eye suggests that the data are indeed correlated in a more-or-less linear fashion, then least-squares regression is a popular method to find the "best" such straight line, by minimizing the sum of squares of the deviations of the data from the line. You can also plot the regression line along with the data
Body Fat % = - 27.38 + 0.2499 Weight (lb)
Does the regression line agree with your eyeball fit?
Does it look like you can use that function to predict the body fat % of a person by knowing his/her weight?

I don't use Minitab, and seldom use ANOVA, so I won't comment on those aspects of the question. [My preferred technique to assess goodness of fit is to compare to a chi^2 distribution, using a Variance/covariance matrix generated by the regression procedure.]
 
You must log in or register to reply here.
Top