Question

Let x be the number of different research programs, and let y be the mean number of patents per program. As in any business, a company can spread itself too thin. For example, too many research programs might lead to a decline in overall research productivity. The following data are for a collection of pharmaceutical companies and their research programs.

x	10	12	14	16	18	20
y	1.9	1.4	1.6	1.4	1.0	0.7

Complete parts (a) through (e), given Σx = 90, Σy = 8, Σx² = 1420, Σy² = 11.58, Σxy = 112.6, and

r ≈ −0.925.

(a) Draw a scatter diagram displaying the data.

(b) Verify the given sums Σx, Σy, Σx², Σy², Σxy, and the value of the sample correlation coefficient r. (Round your value for r to three decimal places.)

Σx =
Σy =
Σx2 =
Σy2 =
Σxy =
r =

(c) Find x, and y. Then find the equation of the least-squares line  = a + bx. (Round your answers for x and y to two decimal places. Round your answers for a and b to three decimal places.)

x	=
y	=
	=	+  x

(d) Graph the least-squares line. Be sure to plot the point (x, y) as a point on the line.

(e) Find the value of the coefficient of determination r². What percentage of the variation in y can be explained by the corresponding variation in x and the least-squares line? What percentage is unexplained? (Round your answer for r² to three decimal places. Round your answers for the percentages to one decimal place.)

r2 =
explained	%
unexplained	%

(f) Suppose a pharmaceutical company has 13 different research programs. What does the least-squares equation forecast for y = mean number of patents per program? (Round your answer to two decimal places.)
patents per program

Answer 1

a)

b)

All values comes out to be the same.

c)

We will be applying the Linear regression model here, it can be done by using the function =LINEST(y_value, x_value, TRUE, TRUE) where y_values contain values of y here and x_values have x values.

Select 5 rows and 2 columns and then write the formula in the first cell and after that, press Shift + Ctrl + Enter.    

The equation comes out to be -
y = 2.92 -0.11*x

d)

e)

The r**2 comes out to be 0.86, which means the change in y can be 86% explained by x.

Explained : 86%

Unexplained : 14%

f)

If x = 13

y = 2.92 -0.11*x = 2.92 - 0.11*13 = 1.54