ARE THE POPULATION VALUES ZERO?


If no linear relationship exists between two variables in the population, the true slope is zero. All of the means of the distributions are the same. Even if the population value is zero, of course, you would not expect the sample value for the slope to be exactly zero. You hope that it would not be too far from zero, though. To test the null hypothesis that the value of the slope is zero in the population, we can calculate the probability of obtaining a slope at least as large as the one we have observed when the null hypothesis is true. As usual, if this probability is small we will reject the null hypothesis that the slope is zero. The observed significance level is based on the t statistic. This t statistic is calculated (like any t statistic) by dividing a sample value by its standard error. In this case, the t values are the sample slope and the sample intercept, divided by their standard errors. In association with this two-tailed t test, there is also a reported significance level for the tests of the hypotheses that the slope and intercept are zero in the population.

When testing whether a linear relationship exists between variables, the important test is the test of the slope. The intercept is simply the value of the dependent variable when the independent variable is zero. All that the test of the intercept tells us is whether the regression line goes through the origin. (The origin is the point at the intersection of the two axes. It is the point where both variables are zero.)




Six Sigma and Beyond. Statistics and Probability
Six Sigma and Beyond: Statistics and Probability, Volume III
ISBN: 1574443127
EAN: 2147483647
Year: 2003
Pages: 252

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