The heighth and collar size c, both in centimeters, measured from a sample of boys were used to create the regression line c = -94 +0.9h. The line is used to predict
collar size from height, both in centimeters, for boys' shirt collars. Which of the following has no logical interpretation in context?
A. The predicted collar size of a boy with height 140 cm
B. The h values in the sample
C. The c values in the sample
D. The slope of the regression line
E. The c-intercept of the regression line

IMO, to say it has "no logical interpretation" is erroneous. Given the units and variable definitions of the problem, it must have a very particular interpretation. Whether that interpretation is useful or not is a different matter, hence the wording used above.

MrRoyal MrRoyal · Answer 2 · 2021-09-27T16:39:02+02:00

The equation of a line of regression is represented as: [tex]^\wedge y =mx + c[/tex].

The context that has no logical interpretation is: (E). The c-intercept of the regression line

Recall that the general equation is:

[tex]^\wedge y =mx + c[/tex]

Where:

[tex]m \to slope[/tex]

[tex]c \to y\ intercept[/tex]

By comparing the above to [tex]^\wedge c = -94 + 0.94h[/tex]

[tex]0.94 \to[/tex] slope of the regression line

[tex]-94 \to[/tex] the y-intercept of the regression line

Also:

h and c represent the h and c values of the sample

Hence, the context with no logical interpretation is option (e)

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