Question

A medical statistician wanted to examine the relationship between the amount of sunshine (x) in hours, and incidence of skin cancer (y). As an experiment he found thenumber of skin cancers detected per 100,000 of population and the average daily sunshine in eight counties around the country. these data are shown...

Average dealy sunshine	5	7	6	7	8	6	4	3
Skin Cancer per 100,000	7	11	9	12	15	10	7	5

a) determine the least squares regression line.

b) interpret the value of the slope fo the regression line.

c) Determine the standard error of estimate

d) is there evidence of a linear relationship, assuming 5% significance level?

e)Estimate Beta1 with 95% confidence.

f)Compute the coefficient of determination (R squared) and interpret this value.

Answer 1

1)
Skin Cancer per 100,000 = -1.1153 + 1.8461*average daily sunshine

2)
slope = 1.846153846
with one unit increase inaverage daily sunshine, there is 1.846 units increase in Skin Cancer per 100,000

3)

SE = sqrt(SSE/(n-2))
SE = 0.960768923

d)
ho: there is no significant linear relationship.
h1: there is significant linear relationship.
with (F=72, P<5%), I reject ho and conclude that
there is significant linear relationship.

e)

I am 95% confident that estimated value beta lie in the interval (1.3137, 2.3785)

f)
R^2= 0.923076923
There is 92.3% variation in the Skin Cancer per 100,000 which is explained by average daily sunshine
this percentage is good and model is said to be a good fit to the data.