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Statistics

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Chapter Seven

Problem 1) Look at the scatter plot below. Does it demonstrate a positive or negative correlation? Why? Is there any outliers? What are they?

Answer 1) The scatter plot above shows a positive correlation, because the variables seem to be moving in a positive slope as can be observed above. There is also an outlier in it, which can be seen above the coordinate 6.00 of the X-Axis. Outliers in statistics are those observations which are placed distant from the rest of the data because of too much variation between them. It deviates markedly from the rest of the set of data, as can be seen in the scatter plot above. It is what is known as an anomaly.

Problem 2) Look at the scatter plot below. Does it demonstrate a positive or negative correlation? Why? Is there any outliers? What are they?

Answer 2) The scatter plot above shows a negative correlation, because the variables seem to be moving in a negative slope from the x axis as can be observed above. There is also an outlier in it, which can be seen at the coordinates (6, 10) of the Axis.

Problem 3) The following data come from your book, problem 26 on page 298. Here is the data:

Mean daily caloriesInfant Mortality Rate (per 1,000 births)

1523154

34956

1941114

267824

1610107

34436

1640153

33627

342944

Problem 3) For the above data construct a scatter plot using SPSS or Excel (Follow instructions on page 324 of your textbook). What does the scatter plot show? Can you determine a type of relationship? Are there any outliers that you can see?

Answer a)

The scatter plot shows random but closely placed observations. The same way they do not have any relationship. Also there are thee outliers which can be observed as seperated from the rest of the data.

Problem 4) Using the same data conduct a correlation analysis using SPSS or Excel. What is the correlation coefficient? Is it a strong, moderate or weak correlation? Is the correlation significant or not? If it is what does that mean?

Answer b)

Mean daily calories

Infant Mortality Rate (per 1,000 births)

1523

154

3495

6

1941

114

1610

24

2678

107

3443

6

1640

153

3362

7

3429

44

2671

7

Correlation

-0.714246811

The correlation coefficient is -0.71. It is a negative correlation of a moderate level, but it is not significant which means that the infants mortality rate per 1000 births have no such relationship with the mean daily calories that they consume.

Problem 5) Bill is doing a project for you in the marketing department. In conducting his analysis regarding consumer behavior and a new product that has come out, he tells you the correlation between these two variables is 1.09. What is your response to this analysis?

Answer 5) There is no such correlation as 1.09. The value of correlation starts from -1 and ends at +1.

Problem 6) Judy has conducted an analysis for her supervisor. The results she obtained was a correlation coefficient that was negative 0.86. Judy is confused by this number and feels that because it is negative and not positive, is means that it is ...

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