1. Multiple linear regression:

Select an outcome (dependent) variable and at least 3 predictor (independent) variables appropriate for a multiple linear regression. Ensure that at least one of your predictor/independent variables is a variable that you would include in the model as dummy (indicator) variable(s).

1. Run descriptive statistics to explore the variables, and recode your dummy variable(s). Interpret your results. ( 3 points)
2. Run a multiple linear regression including appropriate diagnostic tests to examine for assumptions. Interpret your results. (2 points analysis; 5 points discussion of results and diagnostics)

2. Nonparametric tests:

Pick 2 of the following tests, run on appropriate data, and interpret your results ( 2 points each):

1. Spearman's rho,
2. Mann-Whitney U,
3. Kruskal-Wallis analysis of variance
4. Pearson's chi-square.

Hand in your output with annotations (copied to a Word document preferred) and include the syntax. Generally, more description of your logic/work and results is better than less.

Solution:

1. For this model, we’ll use Educ , Size of Place , and Marital Status to predict the variable Respondent’s Income . We’ll use Marital Status as the dummy variable by recoding it in the following way:
   maritcat = 1 if the respondent is married, 0 if not.
   Hence, we are going to estimate the following regression equation:
   $$Income={{\beta }_{0}}+{{\beta }_{1}}Educ+{{\beta }_{2}}Size+{{\beta }_{3}}maritcat+\varepsilon$$
   Using SPSS we get the following results:
   
   The descriptive statistics above show a picture of the main characteristics of the data. Since the three variables we are analyzing are measured at the ratio interval, we use the mean as a measure of central tendency, and the standard deviation as a measure of dispersion.
   For the first variable, Educ , the mean is 13.78 years, and the standard deviation is 2.889.
   For the second variable, Income , the mean is 13.10, and the standard deviation is 5.754.
   Finally, for the third variable, Size of Place , the mean is 416,050, and the standard deviation is 1,309,339.
   Now we show below the distribution of the categorical variable used.
   
   
   Now, we perform a regression analysis:
   
   
   
   The amount of variance explained is approximately 13.1%. This is a bit low, but yet the regression is significant overall, with F = 25.998 and p = 0.000.
   We have the following table with regression coefficients:
   
   The model is therefore:
   $$Income=2.965+0.652Educ+0.000139Size+1.829maritcat$$
   Notice that all the predictors are significant, except for Size , which is not significant (p = 0.457).
   We have the following histogram of residuals:
   
   Now we test for normality:
   
   The p-value for Shapiro-Wilk test is p = 0.000, which means that we have enough evidence to reject the null hypothesis of normality.
   We have the plot of residuals by predicted;
   
   There is some kind of a pattern, which indicates that the heteroskedasticity assumption may be violated.
2. We are interested in testing whether or not Father’s Highest degree is independent from Race . We obtain the following Crosstabulation:

The Chi-Square statistics is 21.797, and the corresponding p-value is p =0.005, which means that we reject the null hypothesis of independence, and hence, we have enough evidence to claim that they are related.

• We are going to test whether or not the median income of male respondents is different from the median income of female respondents. For that purpose we’ll a Mann-Whitney test. Using SPSS we get

The p-value for the test is 0.000, which means that we reject the null hypothesis.

Solution:

Price: $16.49

Solution: The downloadable solution consists of 11 pages, 549 words and 14 charts.
Deliverable: Word Document

▼

Get Solution!

I agree with the Terms & Conditions

All sales are final.