What is the prediction for someone who has a high credit rating and is self-employed?

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Learning Goal: I’m working on a economics practice test / quiz and need an explanation and answer to help me learn.Question 1:
Ignore “income” and “self”. Run a regression of “interest” on “credit”, i.e., predict “interest” using “credit”.
Consider the regression equation: interest = β0 + β1X1 + β2X2 + u
• X1 is binary (1 means “medium” and 0 means “not medium”) X2 is binary (1 means “low” and 0 means “not low”)Answer the following questions:a. We are interested in whether or not “credit” is useful in predicting “interest”. Use the above regressionequation and write down the null and alternative hypotheses.b. We are interested in whether or not the prediction for someone with “credit”=medium is the same asthe prediction for someone with “credit”=low. Use the above regression equation and write down thenull and alternative hypotheses.1c. We are interested in whether or not the prediction for someone with “credit”=medium is the same asthe prediction for someone with “credit”=high. Use the above regression equation and write down thenull and alternative hypotheses.d. In part (b), is the null hypothesis on individual regression coefficients? (Does it involve only one ofβ1 and β2?) If not, transform the regression equation such that we can study the same comparisonin part (b) by testing only one coefficient in the transformed regression. In this case, write down thetransformed regression equation and the null hypothesis based on the transformed regression.Question 2Ignore “income”. Consider the following regression:interest = β0 + β1X1 + β2X2 + β3X3 + β4X1X3 + β5X2X3 + u• X1 is binary (1 means “medium” and 0 means “not medium”)• X2 is binary (1 means “low” and 0 means “not low”)• X3=“self” (X3=1 means “self-employed” and X3=0 means “not self-employed”)Answer the following questions:a. What is the prediction for someone who has a medium credit rating and is self-employed? Write youranswer in terms of β0, β1, β2, β3, β4, β5.b. What is the prediction for someone who has a low credit rating and is self-employed? Write your answerin terms of β0, β1, β2, β3, β4, β5.c. What is the prediction for someone who has a high credit rating and is self-employed? Write youranswer in terms of β0, β1, β2, β3, β4, β5.d. You have a theory: for those that are self-employed, the credit rating does not predict the interest rateof their mortgage. Write down the null and the alternative hypotheses for studying this theory.Question 3Ignore “self”. Consider the following regression:interest = β0 + β1X1 + β2X2 + β3X3 + β4X1X3 + β5X2X3 + u• X1 is binary (1 means “medium” and 0 means “not medium”)• X2 is binary (1 means “low” and 0 means “not low”)• X3 = incomeYou use the above regression to study the effect of income on the mortgage interest rate. Answer the followingquestions:a. You have a theory: for those with a low credit rating, they always get the maximum interest rate,regardless of their income. (In other words, for those with a low credit rating, “income” does not predict“interest”.) Use the above regression equation and write down the null and alternative hypotheses forstudying this theory.b. You are interested in finding out whether or not the effect of income on the interest rate depends on thecredit rating. Use the above regression equation and write down the null and alternative hypotheses.

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