Let's take the example I did in class. Note how the data are set up in columns: the dependent variable (or response) 'y', the independent variable (or regressor) 'x', and, for the one-way ANOVA, a column of indicators for the three groups.
MTB > prin c1-c3
ROW y x group
1 7 10 1
2 9 10 1
3 10 10 1
4 5 17 2
5 7 17 2
6 6 20 3
7 4 20 3
MTB > plot 'y' * 'x'
10.0+ *
-
y - *
-
-
8.0+
-
- * *
-
-
6.0+ *
-
-
- *
-
4.0+ *
-
----+---------+---------+---------+---------+---------+--x
10.0 12.0 14.0 16.0 18.0 20.0
MTB > Regress 'y' 1 'x'.
The regression equation is
y = 12.4 - 0.370 x
Predictor Coef Stdev t-ratio p
Constant 12.353 1.770 6.98 0.001
x -0.3699 0.1143 -3.24 0.023
s = 1.318 R-sq = 67.7% R-sq(adj) = 61.2%
Analysis of Variance
SOURCE DF SS MS F p
Regression 1 18.178 18.178 10.47 0.023
Error 5 8.680 1.736
Total 6 26.857
MTB > Oneway 'y' 'group'.
ANALYSIS OF VARIANCE ON y
SOURCE DF SS MS F p
group 2 18.19 9.10 4.20 0.104
ERROR 4 8.67 2.17
TOTAL 6 26.86
INDIVIDUAL 95 PCT CI'S FOR MEAN
BASED ON POOLED STDEV
LEVEL N MEAN STDEV --+---------+---------+---------+----
1 3 8.667 1.528 (---------*--------)
2 2 6.000 1.414 (-----------*-----------)
3 2 5.000 1.414 (-----------*-----------)
--+---------+---------+---------+----
POOLED STDEV = 1.472 2.5 5.0 7.5 10.0
Finally, we get the ANOVA for regression with a lack-of-fit (LOF) test by combining the two ANOVA tables from MINITAB; the LOF degrees of freedom and sum of squares are obtained either by subtracting the "Error" line of the one-way ANOVA from the "ERROR" line of the Regression ANOVA, or by subtracting the "Regression" line of the Regression ANOVA from the "group" line of the one-way ANOVA.
Analysis of Variance SOURCE DF SS MS F p Regression 1 18.1775 18.1775 8.3896 0.044 LOF 1 0.0129 0.0129 0.0060 0.94 ERROR 4 8.6667 2.1667 Total 6 26.8571
If you are wondering how I got so many decimal places when MINITAB only gave 2 or 3, I got them by doing the calculation by hand.
The conclusion is that there is no evidence (p = 0.94) of non-linearity, hence we can proceed to test the slope of the line and find some evidence (P = 0.044) that the slope is not zero.
If you look over past exams, you will see that questions like those of Assignment 4 count for most of the weight. In addition, there will usually be something on hypothesis testing like Q3 or Q4 of Assignment 3 and a simple theoretical result like Q2 of Assignment 3 or something on probability or properties of distributions from the early weeks of the course.
If you understand the foundations and know how to keep your work organised, these questions are all very simple.
My suggestion is that you concentrate on questions like these. If there is anything you don't understand, you will have to go back and review the fundamental work earlier in the course. Make up new problems. Start by taking the assigned problems and changing the numbers a little or a lot and, when you do that, try to guess how your analysis and conclusions will be affected by the changes. Solve the problems by hand (that is, with your pocket calculator and tables, as you will under exam conditions) and verify your answers by running the same analyses in MINITAB. Next, go to the textbook or the study guide, find more problems like these, solve them by hand, and verify your solutions in MINITAB.
If you are not sure if you have the right method for a given problem, ask me or Dr Rathi to check your work.