Simple regression practice exercises

For each exercise you are given two lists of data. Paste the data into Excel and calculate the regression results, using the A column as the independent variable. Answers are given following the data for each exercises.

1.

            A1       B1
  1:        10       34
  2:        12       41
  3:        14        6
  4:        16        9
  5:        18       31
  6:        20       20
  7:        22       32
  8:        24        1
  9:        26       16
 10:        28       15
 11:        30       20
 12:        32       24
 13:        34       35
 14:        36       33
 15:        38       19
 16:        40       22
 17:        42       50
 18:        44        6
 19:        46       35
 20:        48       35

Slope:    0.206
Intercept:   18.226
R squared:    0.035
Correlation:    0.187
Covariance:   27.400
Squared error: 3116.304
Mean square error:  173.128
Estimated stand dev:   13.158
T statistic:    0.808      18  Degrees of freedom
F statistic:    0.652     1,  18 Degrees of freedom

There is no connection between these variables.

2.

            A2       B2
  1:        10      252
  2:        12      300
  3:        14      348
  4:        16      396
  5:        18      444
  6:        20      492
  7:        22      540
  8:        24      588
  9:        26      636
 10:        28      684
 11:        30      732
 12:        32      780
 13:        34      828
 14:        36      876
 15:        38      924
 16:        40      972
 17:        42     1020
 18:        44     1068
 19:        46     1116
 20:        48     1164

Slope:   24.000
Intercept:   12.000
R squared:    1.000
Correlation:    1.000
Covariance: 3192.000
Squared error:    0.000
Mean square error:    0.000
Estimated stand dev:    0.000

In this case there is a perfect fit.

3.

            A3       B3
  1:        10      286
  2:        12      341
  3:        14      354
  4:        16      405
  5:        18      475
  6:        20      512
  7:        22      572
  8:        24      589
  9:        26      652
 10:        28      699
 11:        30      752
 12:        32      804
 13:        34      863
 14:        36      909
 15:        38      943
 16:        40      994
 17:        42     1070
 18:        44     1074
 19:        46     1151
 20:        48     1199

Slope:   24.206
Intercept:   30.226
R squared:    0.998
Correlation:    0.999
Covariance: 3219.400
Squared error: 3116.304
Mean square error:  173.128
Estimated stand dev:   13.158
T statistic:   94.881      18  Degrees of freedom
F statistic: 9002.455     1,  18 Degrees of freedom

4.

            A4       B4
  1:        10      592
  2:        12      710
  3:        14      408
  4:        16      486
  5:        18      754
  6:        20      692
  7:        22      860
  8:        24      598
  9:        26      796
 10:        28      834
 11:        30      932
 12:        32     1020
 13:        34     1178
 14:        36     1206
 15:        38     1114
 16:        40     1192
 17:        42     1520
 18:        44     1128
 19:        46     1466
 20:        48     1514

Slope:   26.060
Intercept:  194.256
R squared:    0.853
Correlation:    0.924
Covariance: 3466.000
Squared error:311630.376
Mean square error:17312.799
Estimated stand dev:  131.578
T statistic:   10.215      18  Degrees of freedom
F statistic:  104.344     1,  18 Degrees of freedom

5.

            A5       B5
  1:        10     1272
  2:        12     1530
  3:        14      528
  4:        16      666
  5:        18     1374
  6:        20     1092
  7:        22     1500
  8:        24      618
  9:        26     1116
 10:        28     1134
 11:        30     1332
 12:        32     1500
 13:        34     1878
 14:        36     1866
 15:        38     1494
 16:        40     1632
 17:        42     2520
 18:        44     1248
 19:        46     2166
 20:        48     2214

Slope:   30.180
Intercept:  558.767
R squared:    0.463
Correlation:    0.681
Covariance: 4014.000
Squared error:2804673.383
Mean square error:155815.188
Estimated stand dev:  394.734
T statistic:    3.943      18  Degrees of freedom
F statistic:   15.550     1,  18 Degrees of freedom

6.

            A6       B6
  1:        10     8000
  2:        12     6480
  3:        14     5120
  4:        16     3920
  5:        18     2880
  6:        20     2000
  7:        22     1280
  8:        24      720
  9:        26      320
 10:        28       80
 11:        30        0
 12:        32       80
 13:        34      320
 14:        36      720
 15:        38     1280
 16:        40     2000
 17:        42     2880
 18:        44     3920
 19:        46     5120
 20:        48     6480

Slope:  -40.000
Intercept: 3840.000
R squared:    0.036
Correlation:   -0.191
Covariance:-5320.000
Squared error:112358400.000
Mean square error:6242133.333
Estimated stand dev: 2498.426
T statistic:   -0.826      18  Degrees of freedom
F statistic:    0.682     1,  18 Degrees of freedom