Introduction to Statistics and Data Analysis
5th Edition
ISBN: 9781305750999
Author: Peck Olson Devore
Publisher: CENGAGE C
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Textbook Question
Chapter 5, Problem 55CR
The accompanying data represent x = Amount of catalyst added to accelerate a chemical reaction and y = Reaction time:
- a. Calculate the value of the
correlation coefficient , r. Does the value of r suggest a strong linear relationship? - b. Construct a
scatterplot . From the plot, does the word linear provide the most effective description of the relationship between x and y? Explain.
a.
Expert Solution
To determine
Find the correlation coefficient.
Explain whether the correlation coefficient suggest a strong relation or not.
Answer to Problem 55CR
The correlation coefficient is –0.981.
Explanation of Solution
Calculation:
The given data relates to the amount of catalyst added in a chemical reaction, x and the reaction time, y. The correlation coefficient is denoted by r.
Correlation coefficient:
Software procedure:
Step by step procedure to obtain the correlation coefficient using the MINITAB software:
- Choose Stat > Basic Statistics > Correlation.
- Enter the columns of x, y under Variables.
- Click OK in all dialogue boxes.
Output obtained using MINITAB is given below:
Thus, from the output, the correlation coefficient is –0.981.
Interpretation:
A value of the correlation coefficient, r closer to 1 or –1 suggests a strong correlation coefficient, whereas a value closer to 0 suggests a weak correlation coefficient.
Here, the correlation coefficient is –0.981, which is very close to –1. Evidently, the negative sign suggests a negative relationship between the variables, so that, higher values of x are associated to lower values of y.
Thus, the relationship between x and y is a very strong negative linear relationship.
b.
Expert Solution
To determine
Draw a scatterplot of the data set.
Explain whether it is appropriate to describe the relationship between x and y as linear.
Answer to Problem 55CR
The scatterplot of the data set is as follows:
Explanation of Solution
Calculation:
Scatterplot:
Software procedure:
Step by step procedure to draw the scatterplot using the MINITAB software:
- Choose Graph > Scatterplot > Simple > OK.
- Enter the column of y under Y-variables.
- Enter the column of x under X-variables.
- Click OK in all dialogue boxes.
Thus, the scatterplot is obtained.
Interpretation:
A careful observation of the scatterplot reveals that the points do not exactly fall on a straight line. Rather, the points appear to form a curve with a wide arc.
Hence, it is not appropriate to describe the relationship between x and y as linear.
The arc of the curve being very wide, none of the points would fall to far away from a line drawn through the plot. As a result, the correlation coefficient in Part a has a very high negative value.
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GISS
Worksheet 10
Jesse runs a small business selling and delivering mealie meal to the spaza shops.
He charges a fixed rate of R80, 00 for delivery and then R15, 50 for each packet of
mealle meal he delivers. The table below helps him to calculate what to charge
his customers.
10
20
30
40
50
Packets of mealie
meal (m)
Total costs in Rands
80
235
390
545
700
855
(c)
10.1.
Define the following terms:
10.1.1. Independent Variables
10.1.2. Dependent Variables
10.2.
10.3.
10.4.
10.5.
Determine the independent and dependent variables.
Are the variables in this scenario discrete or continuous values? Explain
What shape do you expect the graph to be? Why?
Draw a graph on the graph provided to represent the information in the
table above.
TOTAL COST OF PACKETS OF MEALIE MEAL
900
800
700
600
COST (R)
500
400
300
200
100
0
10
20
30
40
60
NUMBER OF PACKETS OF MEALIE MEAL
Chapter 5 Solutions
Introduction to Statistics and Data Analysis
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