1. Consider the following variables for the 50 states of the United States: Y- p
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Question
1. Consider the following variables for the 50 states of the United States: Y- percentage of each state's population living in households with income below the federally defined poverty level in the year 2002, X1 -birth rate for females 15 to 17 years old in 2002, calculated as births per 1000 persons in the age group, and X2-birth rate for females 18 to 19 years old in 2002, calculated as births per 1000 persons in the age group. (Data source: The U.S. Census Bureau and Mind On Statistics, (3rd edition), Utts and Heckard). Minitab analysis of the data leads to the following results Correlation: Y, X1, X2 X1 X1 0.699 X2 0.627 0.955 Regression Analysis: Y versus Xl, X2 Analysis of Variance Source Regression 2 423.07 211.536 Error Total DF Adj SS Adj MS F-Value P-Value 24·18 0.000 47 411.19 49 834.26 8.749 Coefficients Term Constant X1 X2 1.96 0.192 -0.1023 0.0764 Coef SE Coef T-Value P-Value 0.002 0.002 0.187 3.29 3.30 1.34 6.44 0.632 Regression Analysis: Y versus X1 Coefficients Term Constant X1 Coef SE Coef T-Value P-Value 0.001 0.000 1.32 0.38720.0572 3.40 6.77 4.49 Perform a test to see if the model with both Xi and X2 is significant overall? Use a 0.05. What is your conclusion? What are the consequences of multicollinearity in multiple regression? Is there any multicollinearity that you detect for the model with both X and X2? Do the estimated regression coefficients have the algebraic signs you might expect for the model with both Xi and X2? What about in the model with just X1? a. b. c.Explanation / Answer
a)
Overall the model is significant. But X2 is insignificant as the p- value of the coefficient is >0.05
b)
It will be difficult to interprete the coeffients in case of multi collinearity. Correlation between X1 and X2 is 0.95. So they are highly corelated.
c) Yes.
d) P - value for X1 in both models is less than 0.05. So X1 is significant in both the models
e) Model 2 i.e. only with X1 is better.
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