The flu shot is an effective way to prevent disease during the flu season, but i

Question

The flu shot is an effective way to prevent disease during the flu season, but it may gurantee complete immunity the longer someone portpones the shot. Data was collected from people who waited to get a flu shot and the number (in the thousands) of people that developed flu like symptoms as a result of waiting. Calculate a linear regression line for flu cases as a function of weeks since the vaccine was available and determine whether it is significantly different zero at the =0.05 level of significance.

Weeks since Vaccine was available

3, 6, 7, 9, 4, 2, 3, 10, 7, 4, 8, 10, 9, 3

Flu cases (in the thousands)

11.2, 17.5, 19.4, 21.3, 12.9, 10.1, 10.9, 22.1, 18.1, 13.1, 18.2, 21.2, 20.9, 10.0

A) What is the mean for x? Provide your answer to two decimal places and appropriate rounding.

B) What is the mean for y? Provide your answer to two decimal places and appropriate rounding.

C) What is the slope of the line (b)?. Provide your answer to four decimal places and appropriate rounding.

D) What is the equation for the line? Provide your answer to the right of the equal sign given the following format: y_hat=y_bar+b(x-x_hat). Include parentheses and leave the x variable as 'x', do not include any spaces in your answer.

E) What is the SSTotal ? Provide your answer to four decimal places and appropriate rounding.

F)What is the SSregression ? Provide your answer to two decimal places and appropriate rounding.

G) What is SSresidual ? Provide your answer to two decimal places and appropriate rounding.

H) What is the mean of squares for regression? Provide your answer to two decimal places and appropriate rounding.

I) What is the mean of squares for the residual? Provide your answer to three decimal places and appropriate rounding.

J) What is the F ratio? Provide your answer to two decimal places and appropriate rounding.

K) What is the critical value for an =0.05 given the data?

L)What are the null and alternative hypotheses?

M) Based on the critical and calculated values the null hypotheses should be rejected.

Explanation / Answer

a)Mean(x)=6.07

b)Mean(y)=16.21

c)Slope=1.5786

d)eqn= y=16.21+1.579*(x-6.071)

e)SST=276.69

f)SSreg=266.45

g)SSres=10.24

i)MSres=0.853

j)F=312.24

k)243.9

l)H0:b1=0, Ha:b1=0

m)As 312.24>243.9 , we reject H0 and hence b1=0

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