Question

Data on ICU hospitalization (X) and number of death (Y) for 5 days due to COVID-19 is given.

Date	In ICU (X)	Death (Y)
04/25	50	21
04/26	80	35
04/27	87	31
04/28	92	45
04/29	118	50
Total	427	182

Use the fitted regression model to estimate the number of death when number of patients in ICU is 500 rounded to closest number.

Question 11 options:

	255
	240
	201
	271
	218

Answer 1

Solution:
Regression equation can be written as follows:
Y = a+bx
Here Y is dependent variable i.e. No. of deaths
X is indepenent variable i.e. ICU hospitalization
a is intercept of regression lien
b is slope of regression line
Slope of regression line can be calculated as
slope = ((n*Xi*Yi) - (Xi * Yi))/((n*Xi^2) - (Xi)^2))

X	Y	X^2	Y^2	XY
50	21	2500	441	1050
80	35	6400	1225	2800
87	31	7569	961	2697
92	45	8464	2025	4140
118	50	13924	2500	5900
427	182	38857	7152	16587

Slope = ((5*16587) - (427*182))/((5*38857)-(427*427)) = 5221/11956 = 0.4367
Intercept of regression line can be calculated as
Intercept = (Yi - slope*Xi)/n = (182 - 0.4367*427)/5 = -0.8929
So regression equation is Y = -0.8929 + 0.4367*X
Now If X = 500
than Y = -0.8929 + 0.4367*500 = 217.45 or 218
So its answer is E. i.e. 218