204 14 simp lin reg - Chapter 14 Simple Linear Regression...

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Chapter 14 Simple Linear Regression Hypotheses tests and Confidence Intervals In simple linear regression we assume there is a linear relationship between the explanatory variable (x) and the response variable (y). For example, assume the growth rate (y) of microscopic marine plants is linearly related to the nitrogen concentration in water (x) according to the following equation. y = β 0 + β 1 x (the “hat” above the y indicates the y is a predicted value) However, if we were to actually measure growth rates at specific concentrations we would find that the y values do not all occur on the line. The reason for this is that even though the relationship between nitrogen concentration and growth rate is linear there are other confounding variables (light, temperature, etc.) which we don’t completely control and which add scatter or “noise” to the data. The actual observed y values are therefore described by the following equation: y = β 0 + β 1 x + ε Notice that since we are now dealing with observed
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204 14 simp lin reg - Chapter 14 Simple Linear Regression...

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