7. Run a linear regression for the following data (Arm Span, inches vs. Height,

Question

7. Run a linear regression for the following data (Arm Span, inches vs. Height, inchesy a. Looking at the "Critical values of r Height (in) Arm Span ( 45 60.4 38.2 72.6 52.1 41.8 between the bivariate data? Explain. 39.5 62.7 36.5 73.8 49.5 b. Use linear regression to write an equation for this proportional relationship (Remember what it means to 5 be proportional)? 42.3 32.1 33.6 In the context of this problem, what is the significance of the slope of the regression line from part b? C. d. For the data above (Arm Span, inches vs. Height, inches), explain the coefficient of correlation in your own words For the data above (Arm Span, inches vs. Height, inches), explain the coefficient of determination in your own words. e. f. What are the limitations for our linear model?

Explanation / Answer

a)

use correl function in excel

df =n-2 = 7-2 = 5

critical value = 0.878

since

r = 0.983 > 0.878

we reject the null hypothesis

and conclude that there is relation between height and arm span

b)

height^ = 4.391 + 0.9217 *arm span

c)

when arm span increases by 1 inch, then on average height increase by 0.9217 inch

d)

r = 0.98342

this means there is positive and strong correlation between two variables

e)

coefficient of determination = r^2 = 0.967115659

which means 96.71 % of variation in height is explained by arm span

Please rate

45 39.5 60.4 62.7 38.2 36.5 72.6 73.8 52.1 49.5 41.8 42.3 32.1 33.6 r 0.98342

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