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Hypothesis Tests
Just because we can compute a regression model does not mean that it is a valid model. We can
test whether or not the variable x can meaningfully predict the variable y by running
LinRegTTest to test whether or not B, the population slope coefficient for the model
(approximated by b) is really 0. LinRegTTest is located on the STAT page in the TESTS list.
The test requires the names of the lists containing the data values and what the alternative
hypothesis is.
Example: Income versus Food
Find the least squares regression line for the data on incomes (in thousands) and food
expenditures (in hundreds of dollars) on the seven households given in the following table. (Use
income as an independent variable and food expenditure as a dependent variable.) Find the
coefficient of determination, the linear correlation coefficient, and test at a 1% significance level
whether or not the slope of the regression line for the population would be positive.
Income (x) Food Spending (y)
35 9
49 15
21 7
39 11
15 5
28 8
25 9
We start by entering the data into lists L1 and L2.
Press the STAT key.
Press the number 1 key.
Enter the Income (x) values into L1.
Enter the Food Spending (y) values into L2.
Press the STAT key.
Press the ► key to highlight CALC.
Press the number 8 key.
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