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Attenuation caused by infrequently updated covariates in by Andersen P.K., Liestol K.

By Andersen P.K., Liestol K.

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72. 16, respectively. 6 Tests of Significance and Confidence Intervals The most common hypothesis of interest in simple linear regression is the hypothesis that the true value of the linear regression coefficient, the slope, is zero. This says that the dependent variable Y shows neither a linear increase nor decrease as the independent variable changes. In some cases, the nature of the problem will suggest other values for the null hypothesis. 6 Tests of Significance and Confidence Intervals 17 exactly equal the hypothesized value even when the hypothesis is true.

Seed weight is mean seed weight (grams per plant) from independent samples of four plants. (Data courtesy of Virginia Lesser and Dr. 3 (a) Determine the linear regression of seed weight on radiation separately for each level of ozone. Determine the similarity of the two regressions by comparing the confidence interval estimates of the two intercepts and the two slopes and by visual inspection of plots of the data and the regressions. (b) Regardless of your conclusion in Part (a), assume that the two regressions are the same and estimate the common regression equation.

1 Z = 6 5 B= 15 15  2 4 7 7 5 −1 0 . −2 10 1 1  1 X= 1  1 1  5 6  4  9  2 6 The numbers that form a matrix are called the elements of the matrix. A general matrix could be denoted as   a11 a12 · · · a1n  a21 a22 · · · a2n  . A =  ..   ... .  am1 am2 · · · amn The subscripts on the elements denote the row and column, respectively, in which the element appears. For example, a23 is the element found in the second row and third column. The row number is always given first.

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