Project

MA103 Basic Statistics - Correlation & Regression Project – Fall 2020 Due Date: _________________ In this project, you will discuss what correlation is, what regression lines are, and how each can be determined. You will also be given various sets of data for which you will determine and describe what type of correlation exists. Additionally, you will find regression lines for sets of data and use them to predict other data values. Your project should include: PART 1 – EXPLANATION OF CONCEPTS This is the paper portion of your project. Please include the following discussions/explanations in a paper format (organized into complete sentences & paragraphs, correct grammar & spelling, etc.)

A) A detailed explanation of correlation. Include in your explanation: a definition of correlation, the different types of correlation, how you can determine the type of correlation by looking at a scatter plot, and how you can determine the type of correlation by computing the value of the correlation coefficient, r. Include in your explanation both how the direction and the strength of the correlation can be determined. Include examples to illustrate your explanations.

B) An explanation of what a regression line is. Describe how it is found and what it can be used for.

C) A discussion of the distinction between correlation and causation with respect to data sets. Clearly explain the difference and include examples in your explanation.

PART 2 – CALCULATIONS For each of the following 5 data sets provided to you, please do the following.

A) Use Excel to construct a scatter plot and compute the value of the correlation coefficient. Additionally, the 1st and 5th given data sets have a significant correlation. For these two data sets, also use Excel to

 Add the regression line to your scatterplot

 Find the equation of the regression line

B) Give an explanation of the type of relationship that exists between the two variables. This explanation should include:

 Say whether there is a strong positive linear correlation, weak positive linear correlation, strong negative linear correlation, weak negative linear correlation, or no linear correlation between the two variables.

 Describe how you can see this from the scatter plot and from the value you found for the correlation coefficient.

 Interpret this relationship in the context of the problem.

Additionally, for the 1st and 5th given data sets use your regression line to predict a y-value for the given x-value, and write a sentence explaining this prediction.

o Data set #1 : use x = 85 o Data set #5 : use x = 9

Additional Information:

 Your project should be typed (no hand-written projects!).

 Include all of the sets of data and scatter plots in your report (these can all be copied and pasted into Word from Excel).

 You may reference the textbook, Chapter 9.1 and 9.2, to help with your definition/descriptions. Data Sets: 1. The midterm exam score and the overall grade that 12 students in an elementary statistics course

received.

Midterm Exam Score, x

50 90 70 80 60 90 90 80 70 70 60 50

Overall Grade, y

65 80 75 75 45 95 85 80 65 70 65 55

2. The ages (in years) and the number of hours of sleep in one night for eight adults.

Age, x 35 20 59 42 68 38 75 22

Hours of Sleep, y 7 9 8 6 6 8 5 6

3. The budget (in millions of dollars) and worldwide gross (in millions of dollars) for eight of the most

expensive movies ever made.

Budget, x 207 204 200 200 180 175 175 170

Gross, y 553 391 1835 784 749 218 255 433

4. The body weight (in kilograms) and the brain weight (in grams) for a sample of mammals.

Body Weight (kg), x

52.16 60 27.66 85 36.33 100 35 62 83 55.5

Brain Weight (g), y

440 81 115 325 119.5 157 56 1320 98.2 175

5. The number of years of education and the unemployment rate, according to the U.S. Census Bureau.

Years of Edu., x

5 7.5 8 10 12 14 16

Unemploy. Rate, y

16.8 17.1 15.3 18.7 11.7 8.1 3.8