Question

A researcher wants to determine the relationship between the typing speed of administrative assistants at a major university is related to the time that it takes for the admin assistant to learn to use a new software program and may be used to predict learning time. Data are gathered from 12 departments at the university.

Dept	Typing speed   (words per minute)	Learning time   (hours)
A	48	7
B	74	4
C	52	8
D	79	3.5
E	83	2
F	56	6
G	85	2.3
H	63	5
I	88	2.1
J	74	4.5
K	90	1.9
L	92	1.5

a. Which variable is the response/dependent variable?   

b. Which is the explanatory/independent variable?

c. Develop a scatter diagram for these data. How would you interpret the scatterplot?

Run a regression analysis of the data on Excel. Use your output to answer the following:

d. What is the value of the correlation coefficient between typing speed and learning time? What does is say about the strength of the relationship?

e. What is the value of the coefficient of determination? How would you interpret it?

f. Write the hypotheses for the test of the slope.

g. What is the p-value for the test of the slope? How would you interpret it?

h. What is the least squares regression formula?

i. Use your formula to predict the learning time for an assistant who types 80 words per minute.  

j. Use your formula to predict the learning time for an assistant who types 60 words per minute.

Answer 1

a) the dependent variable in this case will be learning time because we want to predict it on the basis of typing speed.

b) the explanatory/dependent variable is typing speed because we are using it to predict the learning time.

c) the scatter plot of the data is provided below. From the scatter plot we can see a strong linear relationship between the variables which in turn indicates the high value of correlation coefficient.

d) correlation coefficient =-0.974 since this is negative and very close to one there is a strong linear relationship between variables but in opposite direction it means as the typing speed increases learning time decreases.