Question

2.

a. The following data gives the experience of x–ray machine operators and their performance ratings as given by the number of quality x–ray pictures that turned out of 100 pieces.

Experience

16

12

18

4

3

10

5

12

Performance Ratings

87

88

89

68

78

80

75

83

As the Health Statistician of the clinic you have been asked to explain the relationship between these two variables

i. Use a scatter plot to explain the strength of relationship between the variables. 5 marks

ii. Using the data establish the regression model ​​ 10 marks

iii. How will you convince your Director that this model you have given is good enough to make predictions? ​​​​​​​​ 15 marks

Answer 1

i)

From the above scatter plot, increase the value of experience (x), increases the corresponding value of Performance Ratings (y), and vice versa. Hence, these two variables have a positive association.

ii)

	Experience (x)	Ratings (y)	x^2	xy
1	16	87	256	1392
2	12	88	144	1056
3	18	89	324	1602
4	4	68	16	272
5	3	78	9	234
6	10	80	100	800
7	5	75	25	375
8	12	83	144	996
Total	80	648	1018	6727

iii)

From the above probability plot, the residuals follow a normal distribution. Hence, the assumption of the error of the model is satisfied.

The plot between the residuals VS order of the data, it shows randomness without a specific pattern. Hence, assumption of the homoscedasticity on the residual is satisfied.

Therefore, we can convince the Director that this model you have given is good enough to make predictions.