A Medical Statistician Wanted to Examine the Relationship Between the Amount

question 205

Essay

A medical statistician wanted to examine the relationship between the amount of sunshine (x) and incidence of skin cancer (y). As an experiment he found the number of skin cancers detected per 100 000 of population and the average daily sunshine in eight country towns around NSW. These data are shown below. $$\begin{array} { | l | c | c | c | c | c | c | c | c | } \hline \text { Average daily sunshine (hours) } & 5 & 7 & 6 & 7 & 8 & 6 & 4 & 3 \\\hline \text { Skin cancer per } 100000 & 7 & 11 & 9 & 12 & 15 & 10 & 7 & 5 \\\hline\end{array}$$ Find the least squares regression line.

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Definitions:

Sampling Error

The discrepancy between a sample statistic and its corresponding population parameter, due to the fact that the sample is not a perfect representation of the population.

Systematic Error

A consistent, predictable error associated with the measurement process that affects all data points in the same direction.

Non-random Error

Error in data collection or analysis that systematically distorts the results, often due to biased sampling or measurement.

Binomial Distribution

Distribution of probabilities for a binomial variable.