Chapter Seven

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

[pic]

The scatterplot is an example of a positive correlation, the outlier in the scatterplot is 6.00. A ; “Outliners are a set of data, a value so far removed from other values in the distribution that its presence cannot be attributed to the random combination of chance causes” (http://www.statcan.gc.ca/,2013)scatterplot is considered positive when the point runs from the lower left to the upper right such as the circles shown on the example.

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

[pic]
The scatter plot is the opposite of example one, it is actually a negative correlation

because the points run from the upper left to the lower right. As with example one there is an outer liner which is 6.00 as well, it does not fall within line with the other points.

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

Mean daily calories Infant Mortality Rate (per 1,000 births)
1523 154
3495 6
1941 114
2678 24
1610 107
3443 6
1640 153
3362 7
3429 44
2671 7

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

|Mean daily calories |Infant Mortality Rate |
| |(per 1,000 births) |
|1523 |154 |
|3495 |6 |
|1941 |114 |
|2678 |24 |
|1610 |107 |
|3443 |6 |
|1640 |153 |
|3362 |7 |
|3429 |44 |
|2671 |7 |

[pic]

The scatter plot demonstrates that there is a significant reverence between the number of calories and the infant mortality rate; according to the plot if the calorie intake were to increase there would be a decrease in the infant mortality rate. Because the points flow from the upper left to the lower right they show that the correlation is negative. The outliners are demonstrated as a calorie intake of 3,429 and the infant mortality rate of 44, and also a calorie rate of 2,671 and an infant mortality rate of 7.

b) 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?

Excel shows a correlation coefficient of -.9, because of this it is considered to be strong, if the number would have been closer to 0 it would have been considered weak. “The correlation coefficient is a number between -1 and 1, If one variable increases when the second one increases, then there is a positive correlation. In this case the correlation coefficient will be closer to 1; If one variable decreases when the other variable increases, then there is a negative correlation and the correlation coefficient will be closer to -1” (www.medcalc.org, 2014). The correlation shows significant because the data is -9, therefore the calorie intake of infants is very important to their survival.

Problem 4)
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?

I would know that Bill has made a mistake somewhere in his analysis because there is no such correlation of 1.09 they are measured from -1 to +1.

Problem 5)
Judy has conducted an analysis for her supervisor. The result 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 bad. You are her supervisor. How would you clarify this result for Judy regarding the meaning of the correlation?

I would explain to Judy that when dealing with correlations looks can be deceiving and just because a result may be considered negative it does not necessarily mean less. “Although it seems correlation is fairly obvious your data may contain unsuspected correlations. You may also suspect there are correlations, but don't know which are the strongest” (www.surveysystems.com, 2012). I would also explain to Judy that the fact that the analysis shows negative only means that it’s variables move in opposite directions.

Problem 6)

Explain the statement, “correlation does not imply causality.”

Simply put the statement means one variable does not cause the other, there may be times that it would seem likely but there is probable that there is some other reason. (Prinston.edu, 2012).

Problem 7)
Using the best-fit line below for prediction, answer the following questions:

What would you predict the price of Product X in volume of 150 to be (approximately)?

I predict the price of Product X in volume of 150 would be 250.00. If you draw a line to the 150.00 volume to the best fit line and then to the price axis it indicates 250.00

What would you predict the price of Product X in volume of 100 to be (approximately)?

The prediction for Product X in volume of 100 would be 175.00, draw a line from the 100.00 volume to the best fit line and then the price axis and it indicates 175.00.

[pic]

Problem 8)

You are interested in finding out if a student’s ACT score is a good predictor of their final college grade point average (GPA). You have obtained the following data and are going to conduct a regression analysis. Follow instructions on page 324 of your textbook under line of best fit to conduct this analysis.

ACT GPA

22.0 3.0

2.0 3.78

33.0 3.68

21.0 2.94

27.0 3.38

25.0 3.21

30.0 3.65

What is the R? What type of relationship does it indicate (strong/weak; positive/negative)?

|22 |3.00 | |
|32 |3.78 | |
|33 |3.68 | |
|21 |2.94 | |
|27 |3.38 | |
|25 |3.21 | |
|30 |3.65 | |
| | | |
| | | |
|r = |0.984275 | |

[pic]

The relationship between the ACT and the GPA is strong, with the r being r=0.98. The point also goes from the lower left to the upper right.

Go to the coefficients readout. The constant is the intercept. Under that is the ACT and that is the slope. Using the straight line formula of Y = mx + b, which you will find on page 313, you will now predict some future GPA scores: In the formula (m) is the slope; (x) is the variable that you are looking to use as a predictor; and (b) is the intercept. Predict GPA from the following ACT scores using the regression equation/straight line formula (show all your work):

Using the formula x=mx + b, the slope (m-value) is 0.070391949152542 and the intercept (b-value) 1.4665042372881; x is the variable and will be used as the predictor. In order to get the GPA both the m-value and b value will be rounded off making the GPA:

20
Y = mx+b
Y = 0.0704(20) + 1.4665
Y = 1.408 + 1.4665
Y = 2.8745
Y=2.78

25
Y = mx+b
Y = 0.0704(25) + 1.4665
Y = 1.76 + 1.4665
Y = 3.2265
Y = 3.23

34
Y = mx+b
Y = 0.0704(34) + 1.4665
Y = 2.3936 + 1.4665
Y = 3.8601
Y = 3.86

Chapter Eight

Show all your work

Problem 1) A sample of nine students is selected from among the students taking a particular exam. The nine students were asked how much time they had spent studying for the exam and the responses (in hours) were as follows: