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The regression line should be drawn on the scatter diagram in such a way that when the squared values of the vertical distance from each plotted point to the line are added, the total amount will be the smallest possible amount. This criterion is called the Method of Least Squares.
Minimizing the sum of the squared differences of each value of Y from the regression line by the method of calculus, we arrive at two equations, called the normal equations:
Solving these equations simultaneously, and using equivalent expressions for and , we obtain the following formulae used to calculate the coefficients a and b in the regression line = = a + bX
E(Y|X = x) = a + bx
rules for constructing the diagrames
We want to investigate the income data. In the Excel file Midterm Data.xls there is a tab labeled "Income Data 2006". The data in the tab is the income reported by 400 people in
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According to a recent study, when shopping online for luxury goods, men spend a mean of $2,401, whereas women spend a mean of $1,527. Suppose that the study was based on a sample o
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Review the Learning Resources and the media programs related to t tests. For additional support, review the Skill Builder: Research Design and Statistical Design and the Skill Buil
Assumption of extrapolation
A sample of college students and a separate sample of adults aged 30-59 were surveyed regarding the amount of fruit they eat each day. The results are shown in the histograms belo
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