Question

The data shows the number of weeks employed and the number of errors made per day for a sample of assembly line workers.

Weeks (x)	Errors (y)
1	20
1	18
2	16
4	10
4	8
5	4
6	3
8	1
10	2
11	1
12	0
12	1

1. Develop a scatter plot.  Describe the relationship between weeks and errors.
2. Use a simple least square regression equation to predict the number of errors. Is there a significant relationship between weeks and errors?
3. Use a 2nd order (nonlinear) model to predict the number of errors. Is there a significant relationship between weeks and errors?
4. Determine the best model to use for predicting the shipping cost.  Use significant level 0.025.

Answer 1

a) Relationship between weeks and errors :

There is perfect negative association between weeks and errors. As number of weeks increases errors decreases.

b) For simple linear regression model, There is insignificant relationship between weeks and errors.

c) For 2nd order regression model, There is insignificant relationship between weeks and errors.

d) R2 ( 0.9748 ) for 2nd order regression model is higher than simple linear regression model ( 0.8081 ). Therefore 2nd order regression model will be best to use for predicting the shipping cost. ( R2 defines the percentage of Variability explained by independent variable )

Here about 97.48 % of Variability is explained by 2nd prefer model and 80.81 % of Variability is explained by simple linear regression model. PL??