Do exercise #3 in chapter 8 of the Pollock Essentials Textbook [2] The U.S. Depa

Question

Do exercise #3 in chapter 8 of the Pollock Essentials Textbook [2]

The U.S. Department of Agriculture defines a food desert as a census tract in which a sizeable percentage of the tract’s population resides a long distance from the nearest supermarket or large grocery store. 16 Below are fabricated data for ten census tracts. The independent variable is percent low-income residents; the dependent variable is the distance (in miles) between each tract and the nearest grocery store. The hypothesis: In a comparison of census tracts, those with higher percentages of low-income residents will be farther from the nearest grocery store than will tracts having lower percentages low-income residents.

(i) What is the regression equation for this relationship? (ii) Interpret the regression coefficient. What, exactly, is the effect of x on y? (Hint: The table gives information on the independent variable in ten-unit changes: 0 percent, 10 percent, 20 percent, and so on. Remember that a regression coefficient estimates change in the dependent variable for each one-unit change in the independent variable.)

Interpret the y-intercept. What does the intercept tell you, exactly?

Based on this equation, what is the predicted value of y for census tracts that are 15 percent low-income? Census blocks that are 25 percent low-income?

Adjusted R-square for these data is .94. Interpret this value.

Census tract Tract 1 Tract 2 Tract 3 Tract 4 Tract 5 Tract 6 Tract 7 Tract 8 Tract 9 Tract 10 percent low-income (x) 10 10 20 20 30 30 40 40 1.0 1.1 1.3 1.4 1.6

Explanation / Answer

i)

The regression equation is
y = 0.300 + 0.0300 x

ii)

Predictor Coef SE Coef T P
Constant 0.30000 0.06124 4.90 0.001
x 0.030000 0.002500 12.00 0.000

Slope: The estimated p-value of slope is 0.000 and significant at 0.05 level of significance. Hence, we can conclude that for increasing a unit on x increases the mean of y by 0.03.

Intercept: The estimated p-value of intercept value is 0.001 and significant at 0.05 level of significance. Hence, we can conclude that there is any explanatory variables the estimated mean of Y is 0.30.

Based on this equation, what is the predicted value of y for census tracts that are 15 percent low-income?

Ans: The  predicted value of y for census tracts that are 15 percent low-income is

y = 0.300 + 0.0300 *15=0.75

Census blocks that are 25 percent low-income?

Ans:

y = 0.300 + 0.0300 *25 = 1.05.

Adjusted R-square for these data is .94.

Ans: Its mean that 94% information of the Y is explained by the explanatory variable x.

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