Question

7.Listed below are results from two different tests designed to measure productivity and dexterity for randomly selected employees.

Pr oductivity(x) 23 25 28 21 21 25 26 30 34 36

Dexterity(y) 49 53 59 42 47 53 55 63 67 75

a. Plot the scatter diagram below. Label x and y axes. Do a rough sketch.

b. Find the value of the linear correlation coefficient r by the TI83 shortcut- state calculator screen name

c) Test the claim of no linear relation by the TI83 p-value method. α = .05

claim ………………………………................ ________________________

null hypothesis…………………………………. ________________________

alternative hypothesis………………………….. ________________________

Calculator Screen Name……………………… ________________________

test statistic ………………………… ________________________

pvalue/alpha comparison………………………. ________________________

decision …………………………. ________________________

Conclusion …………………………. ________________________ d) Find the estimated equation of the regression line by TI83 shortcut

e) Plot the regression line on the scatter diagram in part a).

f) Assuming a significant linear correlation, predict the score a student would get on dexterity, given he got a 40 on productivity.

g) What percentage of the total variation can be explained by the regression line?

Answer 1

Using TI-84.

a) Press [STAT]->"EDIT", then enter the data in L1 and L2. Set the window settings. Press [GRAPH].

Scatterplot appears below.

b) Press [SAT]->"TESTS"->LinRegTTest and the results are below.

The null hypothesis is

The alternative hypothesis

Test statistics is

P-value/alpha comparison :

We reject the null hypothesis. There is a linear relation.

Productivity and dexterity are linearly related.

d)The linear regression equation is .

e) The regression line on the scatter diagram is plotted below.

f) The linear regression equation is . Thus

g) Since , 97.2% of the total variation can be explained by the regression line.