Data on ICU hospitalization (X
Data on ICU hospitalization (X) and number of death (Y) for 5days 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 deathwhen number of patients in ICU is 500 rounded to closestnumber.
Question 11 options:
|
255 |
|
|
240 |
|
|
201 |
|
|
271 |
|
|
218 |
Answer:
Solution:Regression equation can be written as follows:Y = a+bxHere Y is dependent variable i.e. No. of deathsX is indepenent variable i.e. ICU hospitalizationa is intercept of regression lienb is slope of regression lineSlope of regression line can be calculated asslope = ((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= 0.4367Intercept of regression line can be calculated asIntercept = (Yi- slope*Xi)/n= (182 – 0.4367*427)/5 = -0.8929So regression equation is Y = -0.8929 + 0.4367*XNow If X = 500than Y = -0.8929 + 0.4367*500 = 217.45 or 218So its answer is E. i.e. 218
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