13.5 Interpretation of Regression Coefficients: Elasticity and Logarithmic Transformation

In a linear regression, why do we need to be concerned with the range of the independent (X) variable?

Suppose one collected the following information where X is diameter of tree trunk and Y is tree height.

Regression equation: $\overset{^}{y}_{i} = −3.6 + 3.1 \cdot X_{i}$

What is your estimate of the average height of all trees having a trunk diameter of 7 inches?

The manufacturers of a chemical used in flea collars claim that under standard test conditions each additional unit of the chemical will bring about a reduction of 5 fleas (i.e. where $X_{j} = \text{amount of chemical}$ and $Y_{J} = B_{0} + B_{1} \cdot X_{J} + E_{J}$, $H_{0}$: $B_{1} = −5$

Suppose that a test has been conducted and results from a computer include:

Intercept = 60

Slope = −4

Standard error of the regression coefficient = 1.0

Degrees of Freedom for Error = 2000

95% Confidence…