# multiple regression

## Project Description:

hi jack,

i need some help on 2 multiple regression problems, please. 2-3 days will be fine. let me know how much. thank you.

4 of the questions for each problem are already solved, you'll see on the right side of the excel sheets.

problem 4.6
earnings of mexican street vendors

detailed interviews were conducted with over 1,000 street vendors in the city of puebla, mexico, in order to study the factors influencing vendors' incomes. vendors were defined as individuals working in the street, and included vendors with carts and stands on wheels and excluded beggars, drug dealers, and prostitutes. the researchers collected data on gender, age, hours worked per day, annual earnings, and education level.

write a first-order model for mean annual earnings, e(y), as a function of age (x1) and hours worked (x2).
the model was fit to the data using sas. find the least squares prediction equation on the printout shown below.
interpret the estimated β coefficients in your model.
conduct a test of the global utility of the model (at alpha = 0.01). interpret the result.
find and interpret the value of r_a^2
find and interpret s, the estimated standard deviation of the error term.
is age (x1) a statistically useful predictor of annual earnings? test using α=0.01
find a 95% confidence interval for 〖 β〗_2. interpret the interval in the words of the problem.

problem 4.12
arsenic in groundwater

environmental science and technology (jan 2005) reported on a study of the reliability of a commercial kit to test for arsenic in groundwater. the field kit was to test a sample of 328 groundwater wells in bangladesh. in addition to the arsenic level (micrograms per liter), the latitude (degrees), longitude (degrees), and depth (feet), of each well was measured.

write a first-order model for arsenic level (y) as a function of latitude, longitude, and depth.
fit the model to the data using the method of least squares.
give practical interpretations of the β estimates.
find the model standard deviation, s, and interpret its value.
interpret the values of r^2 and r_a^2
conduct a test of overall model utility at α=0.05
based on the results, parts d-f, would you recommend using the model to predict arsenic level (y)? explain.
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