91影视

A scatterplot of the data is shown below,

If a linear model is adequate, the histogram should be about normal, and the residuals scatterplot should indicate random scatter. The linear model is not appropriate if the residual plot shows a curved relationship.

The using all models to estimate the volume of available pine lumber 30 inches in diameter from a ponderosa pine.

Option 1: Regression line of least square,

$\hat{y}=a+bx$

The coefficients $a$and $b$ are:

$b=0.0042597$

Then the regression line of least square is:

$\hat{y}=2.078+0.0042597x^3$

With $x=DBH$and $y$the yield

Putting the $X$by$30$:

$\hat{y}=2.078+0.0042597(30{)}^3$

$=117.0899$.

Option 2: Regression line is $\hat{y}=a+bx$

The coefficients $a$and $b$are $a=1.2319$and

$b=0.113417$

Then the regression line of least square is

$\hat{y}=a+bx$

The coefficients $a$and $b$are$a=1.2319$

$b=0.113417$

Then the regression line of least-squares becomes:

With $x=$DBH and $y$the yield.

Putting$x$by $30$: $\hat{y}=102.967$.

The prediction that is looks more reliable in part (b).

From the part (b)

Option 1: $\hat{y}=117.0899$

Option 2: $\hat{y}=102.967$

Option 1 provides a more accurate estimate because its residual plot shows no discernible trend, but Option 2's residual plot shows a discernible curve.