Students in a small statistics course wanted to investigate if forearm length (i
ID: 3225247 • Letter: S
Question
Students in a small statistics course wanted to investigate if forearm length (in cm) was useful for predicting foot length (in cm). The data they collected are displayed in the provided scatterplot (with regression), and the computer output from the analysis is provided.
Use three decimal places when reporting the results from any calculations, unless otherwise specified.
The regression equation is Foot (cm) = 9.22 + 0.574 Forearm (cm)
Coef
SE Coef
T
P
9.216
4.521
2.04
0.066
0.5735
0.1578
3.63
0.004
DF
SS
MS
F
P
1
44.315
44.315
13.20
0.004
11
36.916
3.356
12
81.231
Predicted Values for New Observations
Forearm (cm)
Fit
SE Fit
95% CI
95% PI
28
25.274
0.513
(24.144, 26.403)
(21.086, 29.461)
Use the scatterplot to determine whether we should have any significant concerns about the conditions being met for using a linear model with these data. Explain briefly.
Coef
SE Coef
T
P
Constant9.216
4.521
2.04
0.066
Forearm (cm)0.5735
0.1578
3.63
0.004
Explanation / Answer
From the scatter plot we find that most of the data points are scattered around the straight line and the line has an upward trend. There may be linear correlation between forearm length and foot length. To support this we can check the P fort-test for the coefficient of Forearm which is given as .004. This value is less than .01 and .05. We can conclude that at 1% and 5% level of significance there is a linear relationship between the two given variables.
When in scatter plot we find that there is a linear relationship, we can say that there is no significant concern about the conditions being met for using a linear model.