Using r

Power study: An important task for statisticians is to help experimenters decide upon sample sizes for an experiment. This is most frequently done by simulation. Suppose an experimenter has decided on the settings for a two-variable problem, and these are the same as the xs in assign4_i.csv. The experimenter views regression coefficients of 2 (or more) to be of practical interest. Suppose it is known from previous studies that the process experimental standard deviation is s=20. Using a significance level of a=0.05, find the number of replicates of the experiment design (i.e., repeats of the nine x=settings) is needed to detect both variables as significant if they both have an effect size of 2, with power of 0.80 (sometimes called 80% power). (Recall, power = probability of rejecting the null hypothesis, when the null hypothesis is false).

assign4_i.csv

Obs	x1	x2	y
1	1	1	3.540589
2	2	1	8.657852
3	3	1	10.26963
4	1	2	4.884515
5	2	2	9.042827
6	3	2	12.59448
7	1	3	7.525656
8	2	3	9.250009
9	3	3	12.0643