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lm(formula =Length ~ Height) Coefficients: Estimate Std. Error t value Pr(>|t|)

ID: 3157793 • Letter: L

Question

lm(formula =Length ~ Height)

Coefficients:

                        Estimate          Std. Error        t value             Pr(>|t|)   

(Intercept)       222.1093         9.6527             27.050             0.0324

Height             0.257               0.1429             -1.804              0.0713

Residual standard error: 29.22 on 2587 degrees of freedom

Multiple R-squared:  0. 1256,  Adjusted R-squared:  0.08704

4a:  Using the information from the output, write the least squares regression line for this data

4b:  Is the intercept significant?  Is the Height slope significant?  Use alpha=.05

4c:  How much of the variation of this dataset can be attributed to Height?

lm(formula = Length~ Weight)

Coefficients:

                        Estimate          Std. Error        t value             Pr(>|t|)   

(Intercept)       450.308           2.46451           101.565           <.0001

Weight           0.1137             0.04144           -2.746              0.0407

Residual standard error: 29.2 on 2587 degrees of freedom

Multiple R-squared:  0.2907,  Adjusted R-squared:  0.2521

5a:  Using the information from the output, write the least squares regression line for this data

5b:  Is the intercept significant?  Is the Weight slope significant?  Use alpha=.05

5c:  How much of the variation of this dataset can be attributed to Weight?

5d:  Using your least squares equation, what would the predicted Length be for a Weight of 24.4?

Explanation / Answer

4a:

the least squares regression line for this data is

Length = 222.1093 + 0.257 Height

4b:

The p-value corresponding to intercept is 0.0324. Since p-value is less than  alpha=.05 so intercept is significant to the model.

The p-value corresponding to slope is 0.0713 . Since p-value is not less than  alpha=.05 so slope is not significant to the model.

4c:

R-sqaure is 0. 1256 so 12.56% variation of this dataset can be attributed to Height.