(b) Verify the given sums Ex, Ey, E, Ey, Exy, and the value of the sample correlation coefficient r. (Round your value for r to three decimal places.) Ex 90 Ey = 7.9 Ex - 1420 Ey? -11.15 Exy = 112.2 r0.870 (C) Find x, and y. Then find the equation of the least-squares line ŷ - 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- 15 y-1.3167 ý- 2.667 +.09 (d) Graph the least-squares line. Be sure to plot the point (x, y) as a point on the line. y 3 3 2 2 1 5 10 15 20 5 10 15 20 4 3 3 2 2 1 10 15 20 5 10 15 20 -1 o-2 (e) Find the value of the coefficient of determination . 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 to three decimal places. Round your answers for the percent one decimal place.) explained unexplained % (f) Suppose a pharmaceutical company has 14 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

(b) Verify the given sums Ex, Ey, E, Ey, Exy, and the value of the sample correlation coefficient r. (Round your value for r to three decimal places.) Ex 90 Ey = 7.9 Ex - 1420 Ey? -11.15 Exy = 112.2 r0.870 (C) Find x, and y. Then find the equation of the least-squares line ŷ - 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- 15 y-1.3167 ý- 2.667 +.09 (d) Graph the least-squares line. Be sure to plot the point (x, y) as a point on the line. y 3 3 2 2 1 5 10 15 20 5 10 15 20 4 3 3 2 2 1 10 15 20 5 10 15 20 -1 o-2 (e) Find the value of the coefficient of determination . 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 to three decimal places. Round your answers for the percent one decimal place.) explained unexplained % (f) Suppose a pharmaceutical company has 14 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

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Question

Please answer questions E and F

(b) Verify the given sums Ex, Ey, Ex², Ey², Exy, and the value of the sample correlation coefficient r. (Round your value for r to three decimal places.)
Σχ=90
Ey =|7.9
Ex2 =|1420
Ey? =|11.15
Exy =|112.2
r =|0.870
(c) Find x, and y. Then find the equation of the least-squares line ŷ = 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 = |15
y = |1.3167
ý = 2.667
+ 1.09
X X
(d) Graph the least-squares line. Be sure to plot the point (x, y) as a point on the line.
y
y
4
4
3
2
1
1
10
15
20
10
15
20
-1
-1
y
y
4
3
3
2
2
1
1
X
10
15
20
5
10
15
20
-1
(e) Find the value of the coefficient of determination . 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 r to three decimal places. Round your answers for the percent
one decimal place.)
2 =
explained
unexplained
%
(f) Suppose a pharmaceutical company has 14 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

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.
10
12
14
16
18
20
y
1.6
1.5
1.7
1.4
1.0
0.7
Complete parts (a) through (e), given Ex = 90, Ey = 7.9, Ex = 1420, Ey? = 11.15, Exy = 112.2, and r= -0.870.
(a) Draw a scatter diagram displaying the data.
Graph Layers
1.9
After you add an object to the graph you
1.8
can use Graph Layers to view and edit its
1.7
properties.
1.6
1.5
1.4
1.3
1.2
No
1.1
Solution
1
0.9
0.8
0.7
0.6
O Help
9
10
11
12
13
14
15
16
17
18
19
20
21

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