Question

You are given data to analyze for relationship of any kind exists for the latest drug that was proposed. This new drug, XA98 has shown promising results across multiple repeated cross-sectional studies and now combined evidence was gathered to see if any relationships stand out among the multiple tests that were conducted in the past. new chemotherapeutic to eliminate malignant tumors and must determine if a significant 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 mm); 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, 11l

Answer 1

Answer:

To find the relationship between the 4 variables , correlation coefficients between the variables are computed.

The highest correlation is between excitation and tumor_size, correlation r= 0.7362. The relation is positive and significant.

All other pairs of correlation is not significant.

The next highest correlation is between vivi_fluor and tumor_size, correlation r= -0.4185. The relation is negative but not significant.

The correlation is between ultrasono and tumor_size, correlation r= -0.3848. The relation is negative but not significant.

Correlation Matrix
		vivi_fluor	tumor_size	ultrasono	excitation
	vivi_fluor	1.0000
	tumor_size	-0.4185	1.0000
	ultrasono	0.1315	-0.3848	1.0000
	excitation	0.0402	0.7362	-0.1212	1.0000
		10	sample size
		± .632	critical value .05 (two-tail)
		± .765	critical value .01 (two-tail)

Regression is used to predict tumor_size from excitation, vivi_fluor and ultrasono.

The estimated regression equation is

tumor_size =11.231-0.141*vivi_fluor-0.383*ultrasono+0.529*excitation

Only excitation is significantly predicting tumor_size, P=0.0077.

Regression Analysis
	R²	0.800
	Adjusted R²	0.700	n	10
	R	0.894	k	3
	Std. Error of Estimate	14.143	Dep. Var.	tumor_size
Regression output						confidence interval
variables		coefficients	std. error	t (df=6)	p-value	95% lower	95% upper
Intercept	a =	11.231
vivi_fluor	b1 =	-0.141	0.063	-2.252	.0652	-0.295	0.012
ultrasono	b2 =	-0.383	0.293	-1.305	.2396	-1.101	0.335
excitation	b3 =	0.529	0.135	3.926	.0077	0.199	0.859
ANOVA table
Source	SS	df	MS	F	p-value
Regression	4,796.327	3	1,598.776	7.99	.0162
Residual	1,200.073	6	200.012
Total	5,996.400	9