Question

The following table shows the number of full-time faculty that WVU has on staff throughout the years.

Year		# of Faculty
2003		1230
2007		1300
2009		1440
2013		1470
2017		1530
2018		1630

(A) Find the equation of the regression line that represents the number of full-time faculty, F , as a function of x years since 2000. (round the regression coefficients to two decimal places)
F(x) =


(B) What is the correlation coefficient (r-value) for the regression model? (Round your answer to three decimal places)
r =

(C) Given the value of r , does the regression line model the data well? That is, does the equation do a good job of modeling the data?

Yes, the r-value is low, meaning the data can be modeled using a line

No, the r-value is high, meaning the data can't be modeled using a line    

Yes, the r-value is high, meaning the data can be modeled using a line

No, the r-value is low, meaning the data can't be modeled using a line

(D) Using the regression line, How many Faculty members did WVU have in 2010? (Round your answer to the nearest whole number)

Answer 1

(A)

From the given data, the following Table is calculated:

X	F	XF	X2
3	1230	3690	9
7	1300	9100	49
9	1440	12960	81
13	1470	19110	169
17	1530	26010	289
18	1630	29340	324
Total = 67	8600	100210	921

the equation of the regression line that represents the number of full-time faculty, F , as a function of x years since 2000 is given by:

F(X) = 1163.48 + 24.17 x

(B)

From the given data, the following Table is calculated:

X	F	XF	X2	Y2
3	1230	3690	9	1512900
7	1300	9100	49	1690000
9	1440	12960	81	2073600
13	1470	19110	169	2160900
17	1530	26010	289	2340900
18	1630	29340	324	2656900
Total = 67	8600	100210	921	12435200

The correlation coefficient (r-value) for the regression model = 0.964

(C) Correct option:

Yes, the r-value is high, meaning the data can be modeled using a line