Question

In a statistics class, last spring, the students measured their height, their arm span (finger tip to finger tip), and the length of their forearm (elbow to finger tip). All distances were measured in inches.

We collected data to answer this question: Which is a better predictor of someone’s height, their arm span or their forearm length?

In other words, will someone's forearm length or their arm span more accurately predict their height?

Listed below are the data that were collected.

Table of Data: Measurements from students
Student	Arm span	Forearm length	Height
A	60.5	16	62
B	68	17.5	67
C	60	16.6	61
D	64.5	17	65
E	63.5	17	62.5
F	61.5	16.5	62.5
G	67	18	68
H	67	18.5	71.5

create the better linear regression line to predict a person's height. You'll need to do two linear regressions then determine and argue which equation is a "better" model than the other.

determine which model is better. Back up your reasoning with the following (and make sure to do the following:

Use good notation for your regression line equations, including hats.

Use technology to do regression-type calculations and graphs, and include this output in your paper

Correctly create and include scatter plots, including labels in all the right places (include the plots in what you turn in)

Correctly create and interpret a residual plot (include the plots in what you turn in)

Correctly compute and interpret (in a sentence) the correlation coefficients

Correctly compute and interpret (in a sentence) the coefficients of determination

Looked for and "dealt with" outliers in a "statistically responsible" manner

Use the correct response variable

Sufficiently argue which model is better than the other, citing statistical evidence (i.e. all the stuff above)

Answer 1

Hello

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Predicting height using Arm Span

Hence,

The Regression Equation:

The coefficient of correlation, , the height of a person is very strongly and positively related to arm span of a person.

The coefficient of determination,

Residual Plot:

The residual plot is not wildly scattered, hence this regression equation is very much useful.

Predicting height using Forearm Length

Hence,

The Regression Equation:

The coefficient of correlation, , the height of a person is very strongly and positively related to arm span of a person.

The coefficient of determination,

Residual Plot:

Now, after analysis of both the regression equations and other variables, it is clearly evident that the length of forearm is more related to height than arm span or in other words, length of forearm is a better predictor of person's height than their arm span.

I hope this solves your query.

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