Advance Biostats SPSS (Multiple Linear Regression)

PART 1

Step-by-Step Guide Assignment Problem 4.1

Multivariate Linear Regression

Problem 1. Explain the assumptions of Linearity, Sampling independence, Normality, and Homoscedasticity (or equal variance).

a. How would you test whether these have been met? (Note: for the exam you do not need to test these assumptions)

Brief overview:

Assumption of Linearity: For each unit change in the independent variable, there is a constant change in the dependent variable. With multiple linear regression, the mean value of the outcome changes linearly with multiple independent variables.

Test for Linearity: construct a scatter plot of the raw independent variable versus the outcome variable to expose the linear relationship between the two interval-level variables.

Assumption of sampling independence: Each population member has the same probability of being selected into the sample and the selection of any individual into the sample does not influence the likelihood of selecting any other individual. Random sampling strategy usually satisfies this assumption.

Assumption of Normality: The distribution of the continuous outcome variable is normal.

Test of Normality: Produce a histogram to assess distribution pattern of the dependent variable is normal (bell-shaped curve). Normality can also be assumed with sample sizes >100 in most cases.

Assumption of Homoscedasticity: The variance of the outcome variable is equal around the mean for any value of the independent variable.

]

Test for Homoscedasticity: Producing histograms to assess normal distribution of the dependent variable for each level of an interval-independent variable.

b. Using SPSS, test the assumption of Linearity between the independent and dependent variables.

Step 1. Open the data set Practice_Week04_dataset.sav in SPSS.

Step 2. Go to Graphs ( Legacy Dialogs ( Scatter/Dot.

Step 3. Click on the Simple Scatter icon then click Define.

Step 4. Place birth weight [birthw] (the dependent variable) in the Y Axis box. Place age at conception [age] in the X Axis box. Click OK.

SPSS Output:

Step 5. Repeat steps 2 and 3. In step 4, transfer age back to the storage box and replace it with body mass index [bmi] in the X Axis. Click OK.

SPSS Output:

Step 6. Repeat steps 3 through 5, substituting cups per day [coffee] for body mass index [bmi].

SPSS Output:

There appears to be a linear increase in birthweight with increase in age and an obvious increase in birth weight with increase in BMI. The birth weight does not increase or decrease with increase coffee cups per day. The horizontal line produced is linear, but horizontal to the X axis. All variables meet the assumption of linearity.

c. Using SPSS, test the assumption of Normality for the dependent variable.

Step 7. Go to Graphs ( Legacy Dialogs ( Histogram.

Step 8. Place birth weight [birthw] in Variable and check Display normal curve. Click OK.

SPSS Output:

Despite a steep kurtosis, the dependent variable birth weight appears normally distributed.