Statistics Analysis Report

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PSY2110—Online--Research Report #4 Correlation and Regression—15 points

DUE: Due Date on Syllabus

For this report, you will conduct research on some type of relationship between variables. One example of a relationship between variables that you might want to investigate is the number of credit hours a person takes in a given quarter and the number of hours a person spends studying per week. The research questions for this study would be: “Is there a relationship between the number of credit hours a person takes in a given semester and the number of hours he/she studies?” and “Does the number of credit hours a person takes in a given semester predict the number of hours he/she studies?”

Another example of a relationship between variables is examining the relationship between the number of hours worked per week and the number of academic semesters a person expects it will take him/her to graduate. Such a scenario would answer the research questions: “Is there a relationship between the number of hours a person works per week and the number of semesters it takes for him/her to graduate?” and “Does the number of hours a person works per week predict the number of semesters it takes for him/her to graduate?”

For this report, you need to select two continuous, ratio scale variables that you wish to investigate. Be creative, but please be sure that you are asking APPROPRIATE, non-personal questions. Please do not ask your subjects questions about sensitive medical and/or psychological information, illegal behavior, sexual behavior, etc. PLEASE USE YOUR BEST JUDGMENT. You MUST use SPSS to complete this project. 1. Give a brief introductory paragraph on why you chose your research questions. Be sure to write out both of your

research questions. (2 points) 2. Briefly describe EACH of your variables. Which variable is your predictor variable? Which variable is your criterion

variable? (1 point) 3. Collect data from exactly 9 subjects (your friends, classmates via email, family, etc.). Make sure that each subject has

two values, one for the X variable and one for the Y variable. Record your data in a table, then input your data into SPSS.

4. You will use SPSS to analyze your data. Please print out your output when you are complete – you must include it in the materials you turn in.

Entering your data for this project will be similar to how you have entered your data for the previous projects. Keep in mind, however, that for this project you don't have an independent or dependent variable; rather, your two variables are continuous and thus you won't have to define levels.

Correlation:

A. Select analyze  correlate  bivariate B. In the pop-up window:

a. Select your variables by moving them over to the “Variables” column. b. Correlation Coefficients: Select “Pearson” c. Test of Significance: Select “Two-tailed” d. Select “Flag significant correlations” e. Click on “Options”

i. Select “Means and Standard Deviations” ii. Select “Cross-product deviations and covariances”

iii. Missing Values – leave as default (“Exclude cases pairwise”) Regression:

A. Select analyze  regression  linear B. Select your criterion variable and put it in the box marked “Dependent:” C. Select your predictor variable and put it in the box marked “Independent:” D. Click on “Statistics”

a. You should have two boxes checked here: “Model Fit” and “Estimates” b. Click “Continue”

E. Click “OK”

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Here is what your output should look like (with 15 subjects): (Note: We have annotated it for you to help you interpret your output.) Correlations

Regression

Covariance

Correlation Coefficient (r)

Coefficient of Determination (r-square)

Standard Error of the Estimate

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5. Correlation: Now, compute the Pearson correlation (FROM SCRATCH) using the formulas, and verify your

results using SPSS. I know this sounds redundant, but it will help you on the final exam (Trust me). BE SURE TO TYPE YOUR CALCULATIONS INTO YOUR PROJECT a. Create a scatterplot. (1 point) Is the slope for your scatterplot positive or negative? Justify your answer in 1-3 sentences. Scatterplot (in SPSS):

A. Select Graphs  Legacy Dialogs  Scatter/Dot B. In the pop-up window:

a. Select Simple Scatter  Define b. Drag your criterion from “Variables” to the Y-axis in Chart preview c. Drag your predictor from “Variables” to the X-axis in Chart preview d. Click “OK

b. Calculate the covariance by hand. SHOW your work. (1 point)

Double check or verify your answer with your SPSS output. In 3-5 sentences, describe what information the covariance gives researchers.

c. Calculate Pearson’s correlation coefficient by hand. SHOW your work. (1 point) Hint: You don’t need to calculate the standard deviations (unless you want to) – look at the SPSS section

titled “Descriptive Statistics.” Double check or verify your answer with your SPSS output. d. Interpret your correlation. (0.5 point) What does the sign (positive or negative) of the correlation tell you about the relationship? What does the size/magnitude (numerical value) of the correlation tell you about the relationship? e. Hypothesis testing. (1.5 points) Write out your hypotheses in both words and symbols. Set up the criteria for making a decision. That is, find your critical value for an α = .05, two-tailed test. Evaluate the null hypothesis. f. Coefficient of Determination. (1 point) Calculate the coefficient of determination by hand. SHOW your work. Double check or verify your answer with your SPSS output.

Interpret your coefficient of determination in 1-3 sentences. That is, what proportion of the variance does your correlation account for?

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6. Regression Equation. In data analysis, we rarely use univariate (one predictor) regression. As such, writing the regression equation and generating predicted values as we do in PSY2110 is not common. However, it is an important first step for you to learn before you transition to multiple regression.

a. Calculate the slope by hand. SHOW your work. (1 point) Note: You will not be able to verify this answer in SPSS. b. Calculate the y-intercept by hand. SHOW your work. (1 point) Note: You could actually check your work with the regression table “Coefficients” c. Write your regression equation. (1 point) d. Plot your regression line on your scatterplot. (1 point) a) In the SPSS Statistics Viewer window that you get from 5a, (If you do not have this window opened,

please repeat the steps of 5a), double click the scatterplot. In the pop-up window, click the “Add Fit Line at Total”. b) Be sure to plot and label the y-intercept and the line with your regression equation. In the pop-up window of double clicking your scatterplot, click “Add a reference line to the Y axis”. Double click the line that you just add, in the pop-up window of properties, click “Reference Line”,

change the “Position” value to your intercept value and check the “Attach label to line” box. Then, “Apply”. Then, close the scatterplot editor. Then, copy this graph to your report.

One example is as follows:

e. Calculate the standard error of the estimate by hand. SHOW your work. (1 point) Double check or verify your answer with your SPSS output. In 1-3 sentences, interpret the information gleaned from the standard error of the estimate. f. Predicted values. (1 point) Write down your X and Y values for subject 7.

X = Y = Using your regression equation, what is your predicted Y value ( Ŷ ) given your obtained X value for

subject 7? Does this value equal your obtained Y value? How do you account for any discrepancies between the

obtained Y value and the predicted Y value? (In other words, for what reasons may your obtained Y value not equal the predicted Y value?)

Please staple your work together. Please be neat.

Please make sure you have included ALL information requested of you.