Question 7 Suppose that we are interested in explaining variation in consumption

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Question 7 Suppose that we are interested in explaining variation in consumption as it relates to inc and wealth. After collecting the data and running a regression using ordinary least squares (OLs) we obtain the following output: Variable Coefficient Std. Error t-statistic Constant 24.7747 6.7525 Income 0.9415 0.8229 0.0807 -0.0424 Wealth R .9635 R2 .9531 F-stat 92.4019 p-value (0.00000 Based on the information in the above table, please answer the following questions: (a) Fill in the values for the t-statistics and determine which variables are significant at the 95% confidence level. You can use the rule of thumb that if the t-statistic is greater than 2 in absolute value, the variable is significant.

Explanation / Answer

a) To find the t-statistic we need to divide the coefficent value by the standard error.

So t-statistic for constant term is 24.7747/6.7525 = 3.668967

t-statistic for Income variable is 0.9415/0.8229 = 1.144124

t-statistic for Wealth variable is -0.0424/0.0807 = -0.5254027

So here we can see that t-statistic is less than 2 in absolute terms for both Income and Wealth variables, which means that these variables are not significant at 95% confidence level. Only intercept term is coming significant as its t-statistics is greater than 2.

b) We can see that p-value associated with the F statistic is very low so the model is better than the null model.

Also R square is around 0.96 which means that the model is able to explain 96% variance in the response variable.

c) Yes, there seems to be some issue in the model. Though the model is better than the null model and is having high R square value i.e. it is able to explain more than 95% of the variance, both the variables Income and Wealth are not coming significant. Ideally model should only include the terms which are statistically significant.

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