For each of the four sets of data given below (Anscombe.1973), plot y verses x. The data are given in the file Anscombe. Fit a straight line to each of the data sets giving least squares estimates, ANOVA table, and R squared. Compute the correlation coefficient between y and x for each data set. Comment on your results. Would a linear regression of y on x be appropriate in all cases? Discuss.
|
Y1
|
X1
|
Y2
|
X2
|
Y3
|
X3
|
Y4
|
X4
|
|
8.04
|
10
|
9.14
|
10
|
7.46
|
10
|
6.58
|
8
|
|
6.95
|
8
|
8.14
|
8
|
6.77
|
8
|
5.76
|
8
|
|
7.58
|
13
|
8.74
|
13
|
12.74
|
13
|
7.71
|
8
|
|
8.81
|
9
|
8.77
|
9
|
7.11
|
9
|
8.84
|
8
|
|
8.33
|
11
|
9.26
|
11
|
7.81
|
11
|
8.47
|
8
|
|
9.96
|
14
|
8.1
|
14
|
8.84
|
14
|
7.04
|
8
|
|
7.24
|
6
|
6.13
|
6
|
6.08
|
6
|
5.25
|
8
|
|
4.26
|
4
|
3.1
|
4
|
5.39
|
4
|
12.5
|
19
|
|
10.84
|
12
|
9.13
|
12
|
8.15
|
12
|
5.56
|
8
|
|
4.82
|
7
|
7.26
|
7
|
6.42
|
7
|
7.91
|
8
|
|
5.68
|
5
|
4.74
|
5
|
5.73
|
5
|
6.89
|
8
|
- Fit a straight line (regression line) to each of the data sets giving least squares estimates, ANOVA table, and R squared. Interpret the regression line.
- Compute the correlation coefficient between y and x for each data set. Comment on your results
- Display the scatter plot between y and x for each data set.
- Would a linear regression of y on x be appropriate in all cases? Discuss.