- Getting Slope, Y Intercept and Model Utility Test
- Creating Squared terms
- Confidence Interval for average y and Prediction Interval next y
- Best Subsets
- Enter your data. X's should be in several columns and Y should be in the next column.
- Go to Stat, Regression, Regression. The following screen should appear.
- Enter your Y variable as your response. Enter all of your x's as your predictors. Click on o.k.
- The following output should appear.
Creating Residual Plots
Regression Analysis: Energy Conte versus Plastics, Paper, Garbage, Water
The regression equation is
Energy Content = 2245 + 28.9 Plastics + 7.64 Paper + 4.30 Garbage - 37.4 WaterPredictor Coef SE Coef T P
Constant 2244.9 177.9 12.62 0.000
Plastics 28.925 2.824 10.24 0.000
Paper 7.644 2.314 3.30 0.003
Garbage 4.297 1.916 2.24 0.034
Water -37.354 1.834 -20.36 0.000S = 31.48 R-Sq = 96.4% R-Sq(adj) = 95.8%
Analysis of Variance
Source DF SS MS F P
Regression 4 664931 166233 167.71 0.000
Residual Error 25 24779 991
Total 29 689710Source DF Seq SS
Plastics 1 239735
Paper 1 11239
Garbage 1 2888
Water 1 411069
- To create a residual plot, go to Stat > Regression > Regression. Enter your x's and your y's as described above. Then, click on graphs.
Adding a Squared TermSelect either Regular or Standardized. You can only do one at a time. Select histogram and normal plot of residuals. Select the residuals versus the variables and put all the x's that you want for a residual plot. Select O.K. This will give you all of the plots for which you ask. If you want to close all the graphs, go to Windows > Close All Windows.
- First, label a column for the squared term. Click on Calc. The following screen will appear. Put the name of the new column in the first box called Store result in variable.
- In the expression box, enter the expression that you want it to calculate. For instance, x*x will compute the x squared in a new column.
- Click o.k. Your new variable is in the column you just labeled.
- Follow the steps above but before you hit o.k. Go to options. The following screen should appear.
- In the box for Prediction Intervals for new observations, enter your new x's. If you want plastic at 19%, paper at 19%, Garbage at 50% and Water at 48%, enter them in the prediciton interval box.
- If you want to change your condifence, enter that as well in the box below.
- Click O.K.
- Additional lines will be added to your output. It should look similar to the following output below.
- This will give you both the confidence interval and the prediction interval.
New Obs Fit SE Fit
95.0% CI
95.0% PI
1 1361.57
17.68 ( 1325.17, 1397.98) ( 1287.21, 1435.94)
- Follow the steps above but before you hit o.k. Go to options. The following screen should appear.
- In the box for Prediction Intervals for new observations, enter the variables for x. Make sure that you list them in the same order as you listed them in the predictors window.
- If you want to change your condifence, enter that as well in the box below.
- Click O.K.
- Additional lines will be added to your output. It should look similar to the following output below.
- This will give you both the confidence interval and the prediction interval for every item in the orginal data set. .
Predicted Values for New Observations
New Obs Fit SE Fit
95.0% CI
95.0% PI
1 924.18
20.09 ( 882.79, 965.56) ( 847.26, 1001.10)
2 1427.31
10.00 ( 1406.72, 1447.91) ( 1359.28, 1495.35)
3 1430.28
12.79 ( 1403.95, 1456.61) ( 1360.30, 1500.26)
4 1510.45
13.27 ( 1483.13, 1537.77) ( 1440.09, 1580.81)
5 1020.76
12.27 ( 995.49, 1046.03) ( 951.17, 1090.35)
6 1172.56
12.28 ( 1147.28, 1197.85) ( 1102.97, 1242.16)
7 1406.25
9.26 ( 1387.19, 1425.32) ( 1338.67, 1473.84)
8 1639.14
17.49 ( 1603.12, 1675.17) ( 1564.97, 1713.32)
9 1294.31
9.53 ( 1274.68, 1313.94) ( 1226.57, 1362.06)
10 1350.22
9.66 ( 1330.33, 1370.11) ( 1282.40, 1418.04)
11 1067.92
18.09 ( 1030.66, 1105.18) ( 993.13, 1142.70)
12 1289.42
10.64 ( 1267.50, 1311.34) ( 1220.98, 1357.87)
13 1423.09
10.93 ( 1400.58, 1445.60) ( 1354.45, 1491.73)
14 1198.72
11.44 ( 1175.15, 1222.28) ( 1129.73, 1267.71)
15 1164.21
8.36 ( 1147.00, 1181.42) ( 1097.13, 1231.30)
16 1347.08
10.55 ( 1325.34, 1368.82) ( 1278.70, 1415.47)
17 1155.19
11.89 ( 1130.70, 1179.67) ( 1085.88, 1224.49)
18 1482.33
15.03 ( 1451.38, 1513.29) ( 1410.48, 1554.19)
19 1232.44
10.98 ( 1209.82, 1255.06) ( 1163.77, 1301.11)
20 1177.24
19.10 ( 1137.90, 1216.58) ( 1101.40, 1253.08)
21 1253.44
11.96 ( 1228.81, 1278.08) ( 1184.08, 1322.80)
22 1251.91
8.49 ( 1234.43, 1269.38) ( 1184.75, 1319.06)
23 1338.45
9.08 ( 1319.76, 1357.14) ( 1270.97, 1405.93)
24 1210.64
18.92 ( 1171.68, 1249.60) ( 1135.00, 1286.28)
25 1234.34
9.80 ( 1214.16, 1254.52) ( 1166.43, 1302.25)
26 1192.89
10.76 ( 1170.73, 1215.05) ( 1124.37, 1261.41)
27 1179.32
20.31 ( 1137.49, 1221.15) ( 1102.16, 1256.48)
28 1290.27
7.85 ( 1274.10, 1306.44) ( 1223.45, 1357.10)
29 1374.22
8.47 ( 1356.76, 1391.67) ( 1307.07, 1441.36)
30 1399.41
9.87 ( 1379.08, 1419.75) ( 1331.46, 1467.36)
Values of Predictors for New Observations
New Obs Plastics Paper Garbage
Water
1
18.7 15.7 45.0
58.2
2
19.4 23.5 39.7
46.3
3
19.2 24.2 43.2
46.6
4
22.6 22.2 35.8
45.9
5
16.5 23.6 41.2
55.1
6
21.4 23.7 35.6
54.2
7
19.5 24.5 40.2
47.2
8
24.0 19.4 44.1
43.8
9
21.5 23.8 35.4
51.0
10 20.3
26.5 34.2 49.1
11 17.0
23.5 32.5 53.2
12 21.0
27.0 38.2 51.8
13 20.5
19.9 41.4 46.7
14 20.5
23.0 43.6 53.6
15 18.8
22.6 42.2 53.0
16 18.3
21.9 41.5 47.4
17 21.4
20.5 41.2 54.7
18 25.1
22.6 37.0 48.7
19 21.0
26.3 38.7 53.2
20 18.0
28.2 44.2 53.4
21 18.7
29.4 34.8 51.1
22 18.5
26.6 37.6 50.7
23 22.1
24.9 37.1 50.7
24 14.3
26.3 35.8 48.2
25 17.7
23.6 37.4 49.9
26 20.5
26.6 35.4 53.6
27 18.3
13.8 51.3 51.4
28 19.1
25.6 39.5 50.1
29 21.3
20.6 40.7 48.7
30 21.6
22.7 36.2 48.2
- If you would like to determine what are the best subsets of the regression formula. Select Stat, Regression, Best Subsets.
- You should get the following screen.
- Your y is your response variable. Enter the variables that you want to be considered for the regression formula in the Free Predictors box.
- Enter the variables that have to be included in the model in the box "Predictors in all model".
- Click here to see what the output should look like.