3. A U.S. Department of Agriculture defines a food desert as a census tract in w

Question

3. A 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.1 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 Percent low-income (x) Tract 1 Tract 2 Tract 3 Tract 4 Tract 5 Tract 6 Tract 7 Tract 8 Tract 9 Tract 10 .2 .4 .5 10 10 20 20 30 30 40 40 .8 1.0 1.1 1.3 1.4 1.6 1. (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.) 2. Interpret the y-intercept. What does the intercept tell you, exactly? 3. 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 4.

Explanation / Answer

1.

i)

The regression equation of this relationship is,

y = 0.3 + 0.03x

ii)

The interpretation is,

For 1 unit change in x, y changes by 0.03 unit.

2.

The y-intercept is interpreted as,

The mean value of y is 0.3 when x is zero.

3.

Given x=15 then using the regression equation, we get,

y= 0.3 + 0.03 *15 = 0.75

Given x=25 then using the regession equation, we get,

y= 0.3 +0.03*25 = 1.05

4.

Adjusted R2 = 0.94

This means that 94% of the variability of the dependent variable (y) has been explained by our model(or by x).

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