Question

1. 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

Find estimate  βˆ1β^1

2. 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

Find estimate  βˆ0β^0

3. 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.

Answer 1

Solution:
Regression equation can be written as
Y = β^0 +β^1X
Here Y is the dependent variable
X is the independent variable
β^0 is the intercept of the regression line
β^1 is the slope of the regression line
The slope of the 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
Solution(b)
The intercept of the regression line can be calculated as
Intercept = (Yi - Slope*Xi)/n = (182 - 0.4367*182)/5 = -4.64/5 = -0.8929
Solution(c)
Regression equation can be written as
Y = -0.8929 + 0.4367*X
If X = 500
Than Y = -0.8929 + 0.4367*X = -0.8929 + 0.4367*500 = 217.45 or 218