Multiple Regression Laboratory



Applying Multivariate Models to Your Programmatic Research: Data Analysis Sheet

Download and open the data set you used for your Research Project.

Factorial #1 – turning one of your Research Project ANOVAs into a Factorial ANOVA

Two of the analyses you did for your Research Project involved a BG ANOVA, with a 2-group variable and the quantitative “core” variable. In this first factorial analysis, you will use quantitative variable you used as the DV in your Research Project as the DV in this analysis, one of the 2-group variabled from one of your Resarch Project ANOVAs as one IV, and you need to pick one other 2-group variable to use as the other IV. You can form that 2-group IV however you like – you can:

1. use a qualitaitive variable that has 2 groups in the dataset

2. select 2 values of a qualitative variable that has 3 or more groups (select cases)

3. combine groups so that you have a 2-group variable (recode)

4. split a quantitative variable into two groups (usually at the mean – recode)

Fill in the varibale names below:

DV

IV from Research Project (called RPIV) conditions ___________________ & _________________

New IV conditions ___________________ & _________________

What are the three effects in this study, and tell if each is BG or WG

--

--

--

What type of Research Design is this?

Multivariate Analysis

a. Complete the factorial analysis and compose a table (don’t forget the marginal means), a line graph and a bar graph of the data.

Note: We’ll refer to this as “Table 1” below

b. Find the results of the test of the interaction:

F = ____________________ df = ____, _______ p = ___________ MSe ________________ Is there an interaction ???

c. Find the components for the LSDmmd computation, if necessary:

# conditions = ______ n = ________ df error ______ MSe = _______________ LSDmmd = ____________

Show the pattern of the interaction - use the simple effects of RPIV for each if the New IV

• Use , or = to show the pattern of the simple effect of RPIV for those in aaaaaaa

• Use , or = to show the pattern of the simple effect of RPIV for those in bbbbbbb

• Describe the interaction below:

d. Find the results for the test of the Main effect of the RPIV

F = _____________ df = ____, _____ p = __________ MSe _____________ Is there a main effect ?

Show the pattern of this main effect using or = between the corresponding marginal means in Table 1.

We want to check if the main effect of RPIV is descriptive or misleading …

1. Use , or = to show the pattern of the simple effect of RPIV for those in aaaaaaa

2. Use , or = to show the pattern of the simple effect of RPIV for those in bbbbbbb

3. So, is the main effect of RPIV descriptive or misleading?

e. Find the results for the test of the Main effect of the New IV

F = _____________ df = ____, _____ p = __________ MSe _____________ Is there a main effect of Child’s AGe ?

Show the pattern of this main effect using or = between the corresponding marginal means in Table 1.

We want to check if the main effect of Glasses is descriptive or misleading …

• Use , or = to show the pattern of the simple effect of NewIV for 1111111

• Use , or = to show the pattern of the simple effect of NewIV for 2222222

• So, is the main effect of NewIV descriptive or misleading?

f. What did you learn from this factorial analysis that you didn’t from the ANOVA using the RPIV that you did for your Research Project.

Factorial #2 – turning the other of your Research Project ANOVAs into a Factorial ANOVA

In this second factorial analysis, you will use quantitative variable you used as the DV in your Research Project as the DV in this analysis, the other 2-group variable from one of your Resarch Project ANOVAs as one IV, and you need to pick one other 2-group variable to use as the other IV. You can form that 2-group IV however you like – you can:

1. use a qualitaitive variable that has 2 groups in the dataset

2. select 2 values of a qualitative variable that has 3 or more groups (select cases)

3. combine groups so that you have a 2-group variable (recode)

4. split a quantitative variable into two groups (usually at the mean – recode)

Fill in the varibale names below:

DV

IV from Research Project (called RPIV) conditions ___________________ & _________________

New IV conditions ___________________ & _________________

What are the three effects in this study, and tell if each is BG or WG

--

--

--

What type of Research Design is this?

Multivariate Analysis

a. Complete the factorial analysis and compose a table (don’t forget the marginal means), a line graph and a bar graph of the data.

Note: We’ll refer to this as “Table 1” below

b. Find the results of the test of the interaction:

F = ____________________ df = ____, _______ p = ___________ MSe ________________ Is there an interaction ???

c. Find the components for the LSDmmd computation, if necessary:

# conditions = ______ n = ________ df error ______ MSe = _______________ LSDmmd = ____________

Show the pattern of the interaction - use the simple effects of RPIV for each if the New IV

• Use , or = to show the pattern of the simple effect of RPIV for those in aaaaaaa

• Use , or = to show the pattern of the simple effect of RPIV for those in bbbbbbb

• Describe the interaction below:

d. Find the results for the test of the Main effect of the RPIV

F = _____________ df = ____, _____ p = __________ MSe _____________ Is there a main effect ?

Show the pattern of this main effect using or = between the corresponding marginal means in Table 1.

We want to check if the main effect of RPIV is descriptive or misleading …

4. Use , or = to show the pattern of the simple effect of RPIV for those in aaaaaaa

5. Use , or = to show the pattern of the simple effect of RPIV for those in bbbbbbb

6. So, is the main effect of RPIV descriptive or misleading?

e. Find the results for the test of the Main effect of the New IV

F = _____________ df = ____, _____ p = __________ MSe _____________ Is there a main effect of Child’s AGe ?

Show the pattern of this main effect using or = between the corresponding marginal means in Table 1.

We want to check if the main effect of Glasses is descriptive or misleading …

• Use , or = to show the pattern of the simple effect of NewIV for 1111111

• Use , or = to show the pattern of the simple effect of NewIV for 2222222

• So, is the main effect of NewIV descriptive or misleading?

f. What did you learn from this factorial analysis that you didn’t from the ANOVA using the RPIV that you did for your Research Project.

Multiple Regression – Putting all you Research Project Analyses together

Use the “Core” variable from your Research Project as the criterion variable. Put all four variables from your Research Project analysis into a single multiple regression – 2 2-group variables and 2 quantitative variables.

Univariate Analysis

a. Get the univariate statistics for each variable. For quantitative variables get the mean and the standard deviation. For binary variables (2-category qualitative variables) get the n and % for each category. Collect that information in the space below.

|Variable |Mean |Std |

| | | |

| | | |

| | | |

| | | |

Multivariate Analysis

b. Perform the multiple regression analysis and fill in the following

R = ___________ R² = ____________ F = ____________ df = ______, _________ p = __________

|Predictor |b (p) |β |Does this predictor contribute to the multiple |

| | | |regression model? |

| | | | |

| | | | |

| | | | |

| | | | |

c. What is the best single predictor of your criterion? _______________________

d. Which is a better predictor of criterion, the

best singe predictor or the multiple regression model? __________________ why?

e. Name any variables that are correlated with criterion and contribute to the multiple regression model?

f. Name any variables that are correlated with criterion but do not contribute to the multiple regression model?

g. Pick binary predictor and interpret its correlation and its multiple regression weight (preferably a significant predictor).

h. Pick quantitative predictor and interpret its correlation and its multiple regression weight (preferably a significant predictor).

i. Considering “f”, “g”, “h”, and “i” – What did we learn from the multiple regression that we didn’t learn from the set of correlations?

Assignment grade out of 50 points ______________

-----------------------

RPIV

1111111111 222222222

New IV

aaaaaaa

bbbbbbb

RPIV

1111111111 222222222

New IV

aaaaaaa

bbbbbbb

Grading

r & MR Walk-through ______ 10

r & MR On Your Own ______ 40

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öíàÔÐË¿³§˜‰|o|o|o|o|o|o|o|b|b|b|bhD §CJaJmHnHu[pic]h•n:CJaJmHTotal Graded Points ______ - ______ (points lost - why?)

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