Question

The data for XA98 to combat specific cancer tumors can be found below, establish whether or not any significant relationships exist among the variables and describe how strong these relationships are; hint: think about using linear regression to establish any relationships that can be described with a simple model and pinpoint which variables are critical for understanding these relationships. Feel free to use any resources from the web or from your notes.

The dataset consists of four variables, in vivo fluorescence for XA98 (photon arrival time in picoseconds); tumor size (in volume mm³);  ultrasonography for XA98 (in hertz); excitation light for XA98 (in nm)

vivo_fluor: 123, 34, 56, 78, 29, 19, 101, 283, 98, 76

tumor_size: 23, 43, 51, 56, 72, 34, 98, 12, 34, 23

ultrasono: 34, 44, 54, 44, 34, 44, 45, 54, 67, 88

excitation: 110, 112, 114, 112, 113, 114, 224, 112, 115, 111

Answer 1

The hypothesis being tested is:

H0: µ1 = µ2 = µ3 = µ4

Ha: At least one means is not equal

	Mean	n	Std. Dev
	89.7	10	75.95	vivo_fluor:
	44.6	10	25.81	tumor_size:
	50.8	10	16.34	ultrasono:
	123.7	10	35.27	excitation:
	77.2	40	53.66	Total
ANOVA table
Source	SS	df	MS	F	p-value
Treatment	40,782.20	3	13,594.067	6.84	.0009
Error	71,514.20	36	1,986.506
Total	1,12,296.40	39

The p-value is 0.0009.

Since the p-value (0.0009) is less than the significance level (0.05), we can reject the null hypothesis.

Therefore, we can conclude that at least one means is not equal.