Hypothesis Testing Using Bivariate Regression Model


A researcher is interested in explaining American voters’ attitudes toward free trade between the US and other countries. Based on an economic model she postulates that voters with more formal education have job skills that will be in higher demand under free trade; therefore that these voters stand to gain economically from free trade, and thus will be more supportive of it. She conducts a survey in which a group of voters is queried about whether they favor free trade (yes = 1; no = 0) and their level of education. Education is measured as follows: 0 = some HS, 1 = HS graduate, 2 = some college, 3 = college graduate, 4 = some postgraduate coursework.

(a) She wants to estimate a bivariate regression model to determine whether her theory is supported or not. What regression model should she estimate?

(b) The intercept in this regression is a = 0.15 and the slope is bX = 0.10. Interpret both the slope and intercept. Is the intercept meaningful? Explain whether the results provide support for her theory or not.

(c) What value of the dependent variable would her regression predict, if the explanatory variable is at its maximum value?

(d) The standard error of the regression slope is 0.02. This is an estimate since σ of the dependent variable Y is unknown. Can the researcher form a z statistic or a t statistic? What is the value of this statistic, for the null hypothesis that the slope is 0?

(e) Is the slope significantly different from 0 at the 0.05 significance level? Answer yes or no and explain what this means.



The question belongs to Statistics and it discusses about testing hypothesis using bivariate regression model.

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