# Regression and hypothesis testing - Median Income for Familes

Fran's Mart are located throughout Erie, Pennsylvania, the owner would like to expand into other communities in northwestern Penn. and southwestern New York. As part of her presentation to the local bank, she would like to better understand the factors that make a particular outlet profitable. She must do all the work herself, so she will not be able to study all her outlets. She selects a random sample of 15 marts and records the average daily sales (Y), the floor space (area), the # of parking spaces, and the median income of families in that zip code region for each.

The sample information is attached.

a) Determine regression equation

b) What is value of R2(squared)? Comment on the value.

c) Conduct a global hypothesis test to determine if any of the independent variables are different from zero.

d) Conduct individual hypothesis tests to determine if any of the independent variables can be dropped

e) If variables are dropped, compute the regression equation and R2(squared)

Use Excel to solve parts or all of the problem if necessary.

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#### Solution Preview

Solution;

The regression equation form is y=B0+B1*x1+B2*x2+B3*X3

a)let y,x1,x2,x3 denote the variables sales,area,spaces,income.

Then the regression equation is y=1480.74+0.7315*x1+9.99149*x2-2.30826*x3.

b) R2=0.8354. this value can tell us that the model fits the data pretty good.

c)the global hypothesis test is MSR/MSE=3325.56/180.21=18.6 and p-value is 0.0001.so ...

#### Solution Summary

The solution addresses Fran's Mart are located throughout Erie, Pennsylvania, the owner would like to expand into other communities in northwestern Penn. and southwestern New York. As part of her presentation to the local bank, she would like to better understand the factors that make a particular outlet profitable. She must do all the work herself, so she will not be able to study all her outlets. She selects a random sample of 15 marts and records the average daily sales (Y), the floor space (area), the # of parking spaces, and the median income of families in that zip code region for each.

The sample information is attached.

a) Determine regression equation

b) What is value of R2(squared)? Comment on the value.

c) Conduct a global hypothesis test to determine if any of the independent variables are different from zero.

d) Conduct individual hypothesis tests to determine if any of the independent variables can be dropped

e) If variables are dropped, compute the regression equation and R2(squared)