Probability and Statistics (Answer up to 7th decimal point**)

And please give the answer step-by-step as I want to know how to calculate the answer, thanks.

Q2. (14%) A study was conducted to find out how certain disease may affect the body temperature of a patient with the disease. Eight patients with the disease were randomly selected. Their body temperatures (in degrees Celsius) and the degrees of seriousness of the disease (measured with a scale from 1 to 10; 1 is the least serious and 10 is the most serious) were recorded as shown below.

temperature (seriousness): 37.5 (3) & 37.7 (5) & 37.2 (5) & 38.6 (6) & 38.5 (8) & 40.1 (8) & 39.7 (9) & 40.2 (10)

Regression analysis was used to determine how the degree of seriousness may affect body temperature of a patient.

(a) Let =₀+₁ be the regression line. What are the values of b₀ and b₁?

₀=___________ , ₁= ___________

(b) Use the regression line to estimate the body temperature of a patient with degree of seriousness about 7.

(c) The Health Department claims that the patient's body temperature (Y) and his/her degree of seriousness of the disease (X) are positively linearly related. Test this claim at 5% significance level.