Question

The U.S. Department of Agriculture defines a food desert as a census tract in which a sizable percentage of the tract's population resides a long distance from the nearest supermarket or large grocery store. 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.

Census Tract                                                                   Percent-Low Income (x)                                                    Distance in Miles (y)

Tract 1                                                                                            0                                                                                      .2

Tract 2                                                                                            0                                                                                      .4

Tract 3                                                                                          10                                                                                      .5

Tract 4                                                                                          10                                                                                      .7

Tract 5                                                                                          20                                                                                      .8

Tract 6                                                                                          20                                                                                      1.0

Tract 7                                                                                          30                                                                                      1.1

Tract 8                                                                                          30                                                                                      1.3

Tract 9                                                                                          40                                                                                      1.4

Tract 10                                                                                        40                                                                                       1.6

(A.) What is the regression equation for this relationship? 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.)

(B.) Interpret the y-intercept. What does the intercept tell you exactly?

(C.) 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?                                                                                                                        

Answer 1

Answer :- The U.S. Department Agriculture define a food desert as a census tract in which a sizable percentage of the tract's population resides a long distance from the nearest supermarket or large grocery store.

1) The independent variable in 10℅ changes as ( 0℅, 10℅ ans 20℅ )

i) The regression coefficient estimate change in the dependent variable for each one-unit.

• 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 that,

   X = 15

'X' value is using in regression equation ,

y = 0.3 + 0.03X

   = 0.3 + 0.03(15)

   = 0.3 + 0.45

y = 0.75

Given X = 25

'X' value is using in regression equation,

y = 0.3 + 0.03(25)

   = 0.3 + 0.75

y = 1.05

4) Given adjusted R²= 0.94

This means that 94℅ of the variability of the dependent variable 'y' has been explained by our model.

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