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Use the data in DISCRIM to answer this question. These are ZIP code-level data on prices for various items at fast-food restaurants, along with characteristics of the zip code population, in New Jerseyand Pennsylvania. The idea is to see whether fast-food restaurants charge higher prices in areas with a larger concentration of blacks.(i) Find the average values of prpblck and income in the sample, along with their standard deviations. What are the units of measurement of prpblck and income?(ii) Consider a model to explain the price of soda, psoda, in terms of the proportion of the population that is black and median income:$$p s o d a=\beta_{0}+\beta_{1} p r p b l c k+\beta_{2} i n c o m e+u$$Estimate this model by OLS and report the results in equation form, including the sample sizeand $R$ -squared. (Do not use scientific notation when reporting the estimates.) Interpret the coefficient on prpblck. Do you think it is economically large?(iii) Compare the estimate from part (ii) with the simple regression estimate from psoda on prpblck.Is the discrimination effect larger or smaller when you control for income?(iv) A model with a constant price elasticity with respect to income may be more appropriate.Report estimates of the model$$\log (p s o d a)=\beta_{0}+\beta_{1} \text { prpblck }+\beta_{2} \log (\text { income })+u$$If prpblck increases by .20$(20$ percentage points), what is the estimated percentage change inpsoda? (Hint: The answer is $2 . x x,$ where you fill in the "xx.")(v) Now add the variable prppov to the regression in part (iv). What happens to $\hat{\beta}_{\text {prpblck}} ?$(vi) Find the correlation between log(income) and prppov. Is it roughly what you expected?(vii) Evaluate the following statement: "Because log(income) and prppov are so highly correlated?they have no business being in the same regression."

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Chapter 3

Multiple Regression Analysis: Estimation

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huh? Problem? Ch computer excised from chapter three. We're using the data. Such discrimination. And the first thing we're asking is to find the average size of proportion black and income in the temple every week. Dear, uh, standard deviations. All right, so, uh, it's just summarized the variables. Proportion of black people, immediate income on the price of soda. Lt's something we're gonna need later on. So we see that, uh, proportion is goes from zero to 0.98 in maximum, and me in the average off. This is 0.11 in the day there. And so this is proportional percent that you have to be careful about that. It is varies between human and want, not you, and hundreds and income is the median family income. And that goes home almost 16,236 thousands and has an average off $47,000. And the price of soda the average price of someday just like $1 and can also see you two standard deviations here. Okay, so he had two units of measurements are gonna be important. So the proportion we just have ratios, and it's gonna be in between zero and one an income it in terms of dollars, which usually usually is like Tom's off. I don't know. It's just that they're just dolls. All right. Okay, So the second part of the question is asking us to estimate this model when the price of soda is related to the black proportion and income. Okay. And, uh, we're on this regression. I'm gonna show you the results. So this their aggression price of soda on proportion, Black and income. So the constant, which is because your head is 0.9 to 5. We put them here. Beta, one hand, which is the coefficient of proportion. Black ISS 2012. I'm going alone. Um, yeah. And the coefficient on income is 1.6 times 10 to the power minus six. This is what it means. So is 1.6 times 10 to the power man, it stinks. Is the question Don't come. Okay. And, uh, our squares from this Russian is See, it is 0.6, and we also asked to into Prince the coefficient on proportion. Black on dhe. The question is, do you think is economically large? So the question here is 0.11 0.11 49. And so we have to remember this proportion is ratio between between zero and one. So going from, like 10% 11% ID. Actually, great ratio points 10 ten 2.11. So a 1% changes in terms of proportion is change. 0.1. So this means that a change of 1% will have ineffective 0.11 times point No one which is gonna be 0.0, you have money dollars Surprising. So dating dollars. So in terms off scent, it's gonna be 0.11 cents. So a 1% change in the proportion black is gonna increase the price of soda by 0.11 cents. And if you remember, and the summary statistics price of sort of waas just on average, $1 just like hundreds 10. So change in proportion of in percentage of what? 1% has an effective less than 1% in price of soda. I just like 0.1%. So that's it. Clinically not large. Okay, so the third party is asking us to run a simple aggression of price of sort of proportion black and compare the coefficients two the first progression. So we do that and I have this aggression here. So this is just a simple progression of price of soda on the proportion of black. And he will see that constant because your head is one point. Is your tree Come, beta? One hat is 0.6 All right, so and a question it is. We're one of these to compare this to this model, which we include income. Right? We see that the coefficient when we include income 0.11 it's higher than when we don't include income 0.6. So this commission of fact here is larger will meet, include, well, you control for you Come. All right. So part for is a model with a constant Alice Price of us Still respect income. We here we have If the price of subtle we have the log off price of soda and income. We had a lot of income and, uh, so we run this progression, and I'm just gonna put the results is here. So this progression off Log of price of soda proportion, black and love of income on dde Look at the politicians Come Negative points. 79 coefficient of proportion. Black is 0.12 questioned of low income is Queen 07 my marriage. And, uh, another part of this question is, if proportion black increases by 0.20 which is a 20% points, what is estimated percentage change in the price of soda. So when the proportion black increases by 0.20 what does this make the change admitted Percent change in the price of soda. So we're just gonna multiply the coefficient of purport own proportion black by the amount of change with this 0.20 and his price of storage in log terms. And then we also gonna multiply this number by 100 if you remember correctly. So the percent of change just let me write it here in the price of soda is gonna be 100 times. This is because price of sordid in lark terms and proportion Black March son reduced because of that times coefficient times the change in proportion like and this is gonna be under times 0.12 times point 20. Uh, yeah, 2020 which is gonna be equal to 2.4. So that is when proportion black incredible. 20% points on the price of soda includes by 2.4%. Okay, that's what this was all important for and now, in part five, In addition to it available, we already have also going to include proportion that is living in poverty. And, uh, we're gonna estimate when I look at what happens to the coefficient of proportion black. So for that one, we have the progression here, I believe. Yep. Remember grassing log of try soda in proportion black log off income and we'll include portion that is living in poverty. The coefficient on proportion black. There is no 0.7 and before that, it waas 0.12. So it went down from 0.12 2.7. So coefficient on proportion. Black goes down. And when we include portion poverty as an explanatory variable support six is asking us to find a correlation between Mark incoming proportion palm ity, which I find it here. So it is put a coronation like incoming proportion quality. And this is the coronation. But we in proportion polity and mark income, which is minus 0.84. That's put that heals minus 0.84. Is it roughly what we expected? So this is the very strong negative correlation between month along, income goes up proportion living in poverty. It was done, which is something you'd expect because for the quality we just have a threshold. And if you blow the treasure, lt's because it did prove considered getting in poverty. And if the medium income goes up, this means that more people have higher incomes of more people are above the treasure. So the proportion that is living in politics go down. So this is roughly what we would expect it. So the last part is asking us to evaluate the following statements. Stick with these because large income and proportion poverty are so highly correlated, they have no business being in the same regression. This is Ah, what a valid statement, I would tell you. Because so if these two tables had perfect correlation, meaning that if the coalition was recalled to either one point away minus one point at all, Dan would actually have a problem. We wouldn't even be able to get correct estimates. But they're just highly call it. They're not perfect. Call it. We can include them in the same row corruption. And in fact, if we don't include them, then we would have wanted table by us. Orange Hope that helps take for watching

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