   Chapter 4.2, Problem 16P Understanding Basic Statistics

8th Edition
Charles Henry Brase + 1 other
ISBN: 9781337558075

Solutions

Chapter
Section Understanding Basic Statistics

8th Edition
Charles Henry Brase + 1 other
ISBN: 9781337558075
Textbook Problem

Research: Patents The following data are based on information from the Harvard Business Review (Vol. 72, No. 1). 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 1.8 1.7 1.5 1.4 1.0 0.7 Complete parts (a) through (e), given Σ x = 90 ,   Σ y = 8.1 ,   Σ x 2 = 1420 ,   Σ y 2 = 11.83 ,   Σ x y = 113.8 ,  and  r ≈ − 0 .973 .(f) Suppose a pharmaceutical company has 15 different research programs. What does the least-squares equation forecast for y = mean number of patents per program?

(a)

To determine

To graph: The scatter diagram.

Explanation

Given: The data which consists of variables, ‘the number of different research programs and ‘the mean number of patents per program, represented by x and y, respectively is provided.

Graph:

Follow the steps given below in Excel to obtain the scatter diagram of the data.

Step 1: Enter the data into Excel sheet. The screenshot is given below.

Step 2: Select the data and click on ‘Insert’. Go to charts and select the chart type ‘Scatter’...

(b)

To determine

To test: Whether the provided values of x, y, x2 ,y2, xy and r are correct or not.

(c)

To determine

To find: The values of x¯,y¯, a, b and the equation for the least-squares line.

(d)

To determine

To graph: The least-squares line on the scatter diagram which passes through the point (x¯,y¯).

(e)

To determine

The value of r2, the percentage of variation that can be explained and the percentage of variation that is unexplained.

(f)

To determine

To find: The least square equation forecast.

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