Question

A linear regression model is generated to predict the daily increase in covid 19 cases in Mumbai .

y=2 X1 + 10 X2 + b(100)

where Y= number of new cases daily, X1= no of incoming passenger flights in Mumbai, and X2= no of passenger train arriving in Mumbai; b= constant or predicted daily increase due to community transmission ,even if no passenger flight or trains are allowed into the city .

Assume a1 and a2 are regression coefficeint for X1 and X2 .

a) state the null and alternative hypothesis for the regression model.

b)how many new cases will be added to the daily count if the null hypothesis is true?

c) the p values of a1 and a2 are 0.04 and 0.06 respectively .alpha value is 0.05 .what is the hypothesis testing conclusion for the two regression coefficients ?

Answer 1

Here, y = daily increase count of covif 19 patients in Mumbai

then regression equation of Y = 100 + 2 * X1 + 10 * X2 or y = 100 + a1*X1 + a2*X2 (say)

where, 100 is the no. of increase that will happen with or without any travel from community transmission,

X1 is the no. of ppl using flights and X2 is the no. of passengers in train

Then,

a). Ho : The model is not significant or passengers (flight/train) has no significant effect on Covid 19 cases

or a1 and a2 = 0 (both)

H1 : The model is significant or passengers (flight/train) has significant effect on Covid 19 cases or a1/a2 0 (any one of them)

b). If Ho is true, then a1 = a2 = 0

Y = 100 + 0 * X1 + 0 * X2 = 100 is the no. that will be added to daily count.

c). We reject Ho when p-value < alpha (0.05)

for a1, p-value = 0.04 ( < 0.05). We reject Ho or we can say that X1 = no. of flight passengers is significant at 5% level of significane.

for a2, p-value = 0.06 ( not less than 0.05). We fail to reject Ho or can say that X2 = no. of train passengers is not significant at 5% level of significance.

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