Mr. X is a resident of Wakanda Ward who is concerned with the recent low turnout in local elections in this area. In an effort to understand the occurrence, Mr. Mbewe conducted research investigating the factors that drive an individual’s decision to participate in voting at Local Government level. He has managed to conduct and obtain an output from Stata but is struggling with results interpretation. The following are the output results from Stata: RSS = 28238.59 TSS= 35570.90 Adjusted R-squared = 0.2016 Constant = -0.762 Independent Variable Coefficient Standard Error P-value Income (in Kwacha) 0.310 - 0.003 Age (years) 0.358 0.289 - Years in School 0.900 - 0.010 Female (dummy for female) -0.231 - 0.090 Married (dummy for married) 0.832 - 0.000 Number of school going children in the house -0.532 - 0.002 Assist Mr. X in interpreting the above Stata output results by answering the following questions: a). Using the information above, calculate the R-squared and explain its meaning to Mr. X? c) Is the R-squared a good measure of model fit? Explain your answer and give Mr. X another alternative(s) of model fit measure that he can use? c). In the information Mr. X has given you, some independent variables have pvalues. Use these p-values to tell Mr. X which of his model independent variables are significant. And for each significant variable, interpret their relationship with the dependent variable given that his model is in level-level form. d). The age independent variable in the information above has no p-value, therefore, its significance cannot be determined using the p-value technique conducted in (c). However, Mr. X is very interested in knowing if the influence of age on the dependent variable (Voting at Local Government) is statistically significant. Remembering the Econometrics principles, you suggest the use of the hypothesis testing technique. Demonstrate to Mr. X how to conduct the hypothesis testing process using the t-test. Use 5% level of significance which gives 1.96 critical values. Indicate and explain all the steps involved in the process. e). As a final question, explain to Mr. X the meaning of the constant in a linear regression model.
Mr. X is a resident of Wakanda Ward who is concerned with the recent low turnout in local elections in this area. In an effort to understand the occurrence, Mr. Mbewe conducted research investigating the factors that drive an individual’s decision to participate in voting at Local Government level. He has managed to conduct and obtain an output from Stata but is struggling with results interpretation. The following are the output results from Stata:
RSS = 28238.59 TSS= 35570.90 Adjusted R-squared = 0.2016 Constant = -0.762
Independent Variable Coefficient Standard Error P-value
Income (in Kwacha) 0.310 - 0.003
Age (years) 0.358 0.289 -
Years in School 0.900 - 0.010
Female (dummy for female) -0.231 - 0.090
Married (dummy for married) 0.832 - 0.000
Number of school going children in the house -0.532 - 0.002 Assist Mr. X in interpreting the above Stata output results by answering the following questions:
a). Using the information above, calculate the R-squared and explain its meaning to Mr. X?
c) Is the R-squared a good measure of model fit? Explain your answer and give Mr. X another alternative(s) of model fit measure that he can use?
c). In the information Mr. X has given you, some independent variables have pvalues. Use these p-values to tell Mr. X which of his model independent variables are significant. And for each significant variable, interpret their relationship with the dependent variable given that his model is in level-level form. d). The age independent variable in the information above has no p-value, therefore, its significance cannot be determined using the p-value technique conducted in (c). However, Mr. X is very interested in knowing if the influence of age on the dependent variable (Voting at Local Government) is statistically significant. Remembering the Econometrics principles, you suggest the use of the hypothesis testing technique. Demonstrate to Mr. X how to conduct the hypothesis testing process using the t-test. Use 5% level of significance which gives 1.96 critical values. Indicate and explain all the steps involved in the process.
e). As a final question, explain to Mr. X the meaning of the constant in a linear regression model.
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