Question

A manufacturing company is interested in predicting the number of defects that will be produced each hour on the assembly line. The managers believe that there is a relationship between the defect rate and the production rate per hour. The managers believe that they can use production rate to predict the number of defects. The following data were collected for 10 randomly selected hours.

Defects (Y)	Production rate per hour(X)
2	40
3	45
1	35
2	37
3	40
2	40
3	45
2	30
1	30
4	30

1. Construct a scatter plot diagram and comment on the relationship between y and x

2. Calculate the correlation coefficient (r) between x and y and comment on the result.

3. Find the coefficient of determination r2 and interpret the result.

Answer 1

a)

It looks like there is very weak linear relationshipt between y and x


Very weak positive relationship between x and y since value of r is very close to 0 and is positive
c) Coefficient of Determination(R-squared):
It gives the measure of how close the data points are to the best fit line. In other words, it gives the proportion of variability in dependent variable that can be explained by the independent variable. Higher the Rsquared value, better the model is.

Only 0.073 variablity in dependent variable that can be explained by the independent variable
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