Question

You are given data to analyze for a new chemotherapeutic to eliminate malignant tumors and must determine if a significant 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.

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

here y=dependent varible=excitation

x=vivo_flour,tumour_size,ultrasono

lm in R t o fit a linear regression

Rcode is

vivo_flour <- c(123,34,56,78,29,19,101,283,98,76)
tumour_size <- c(23,43,51,56,72,34,98,12,34,23)
ultrasono <- c(34,44,54,44,34,44,45,54,67,88)
excitation <- c(110,112,114,112,113,114,224,112,115,111)
regressionmod <- lm(excitation ~ vivo_flour+tumour_size+ultrasono)
summary(regressionmod)

Outptut:

lm(formula = excitation ~ vivo_flour + tumour_size + ultrasono)

Residuals:
Min 1Q Median 3Q Max
-28.4049 -11.6601 -0.0958 13.4962 28.0154

Coefficients:
Estimate Std. Error t value Pr(>|t|)   
(Intercept) 22.6791 38.2387 0.593 0.57478   
vivo_flour 0.1995 0.1096 1.820 0.11858   
tumour_size 1.3595 0.3463 3.926 0.00775 **
ultrasono 0.4428 0.5011 0.884 0.41090   
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 22.66 on 6 degrees of freedom
Multiple R-squared: 0.7248,   Adjusted R-squared: 0.5872

F-statistic: 5.268 on 3 and 6 DF, p-value: 0.04059

From output:

significant variable is tumour_size as p= 0.00775 ** and p<0.05

significant at 5% ;level

For variable vivo_flour p=0.11858,p>0.05 ,not significant variable

For variable ultrasono,p=0.41090 and p>0.05,not significant variable

Final regression model is

excitation =22.6791+0.1995 *vivo_flour +1.3595 *tumour size+0.4428 *ultrasono