Scatterplot #1 Simple linear regression results: Dependent Variable:
Volume Independent Variable: Height Volume = -87.123614 + 1.5433498
Height Sample size: 31
R (correlation coefficient) = 0.59824965
R-sq = 0.35790265
Estimate of error standard deviation: 13.396982
Parameter estimates:
Parameter Estimate Std. Err. Alternative DF T-Stat Intercept(y) -87.123614 29.273122 ?0 29 -2.9762324 0.0058 1.5433498 0.38386927 ?0 29 4.0205088 Slope (b) Analysis of variance table for regression model:
Source DF SS MS F-stat P-value Model 1 2901.1889 2901.1889 16.164491 0.0004 Error 29 5204.895 179.47914 Total 30 8106.0839 P-value 0.0004 Calculate, report, and draw conclusions:
3. Answer these questions. Round all numbers to the nearest hundredth.
a. Identify whether each variable is an independent or dependent variable.
The dependent variable is the volume, which means it can change, and the independent variable is the height,
(which may not change).
b. What is the shape of the scatterplot? Does it look linear? Describe any points that appear to be outliers.
The scatterplot is to the right and looks linear. The linear is the shape of the line and show the strength of the
relationship. There is a positive relationship because the variables are moving in the same direction. There is a
weak trend in the first scatterplot. On the second scatterplot, there is the line is linear and forms a straight line. c. Use the slope and intercept that you wrote down in part 1c to write the equation of the regression line in
slope-intercept form.
d. Based on that linear equation, what volume would you predict for a tree that is 77 feet tall? If you graphed a
point for that tree with the predicted volume, where does that point fall compared with the graph of the line?
e. What is the correlation between x and y? Based on the data only, does a higher height cause trees to have a
larger volume? Do you think that tree height is a good predictor of volume?
f. Is the intercept meaningful for this graph? Why or why not?
4. Write three additional observations of the graphs and the statistics you calculated, identifying what you can
learn about the two variables and their relationship.
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