STATISTICS COURSEWORK

Statistics coursework

Statistics coursework

Solution 1:

a) Regression Equation

Total Cost = 8817 + 5.79*output

b) Slope = 5.79, Intercept = 8817

The slope is 5.79. This means that for every additional output, you can expect an average of 5.79 additional outputs per month. The y-intercept 8817 has meaning in this case. We can say that the average number of cost per month in an area with no output is 8817.

c) Correlation Coefficient of total cost and output is .879 which indicates a strong relationship among these variables. The primary meaning of the coefficient of correlation lies in the amount of variation in one variable that is accounted for by the variable it is correlated with.

d) R-sq = 77.2%, R-sq(adj) = 76.7%

In our model, the r-sq interpretation is that almost 77% of the variability in the amount of total coat is explained by the output.

R-squared adjusted is the version of R-squared that has been adjusted for the number of predictors in the model. R-squared tends to over estimate the strength of the association, especially when more than one independent variable is included in the model.

R-sq indicates that 77.2% of the data points lie on the line so we can say that the line is best fitted.

e) Hypothesis:

Ho: Total test is dependent on output.

Ha: Total test isn't dependent on output.

By analyzing one way ANOVA on the data set of total cost and output we reject null hypothesis as p value is less than .05 and conclude that total cost isn't dependent on output.

f) We use Minitab to predict future values of total cost.

g) Assessing accuracy of the model is best accomplished by analyzing the standard error of estimate (SEE) and the percentage that the SEE represents of the predicted mean (SEE %). The SEE represents the degree to which the predicted scores vary from the observed scores on the criterion measure, similar to the standard deviation used in other statistical procedures. According to Jackson, (10) lower values of the SEE indicate greater accuracy in prediction. Comparison of the SEE for different models using the same sample allows for determination of the most accurate model to use for prediction. SEE % is calculated by dividing the SEE by the mean of the criterion (SEE/mean criterion) and can be used to compare different models derived from different samples.

Solution 3:

Period(t)

Sales(Y)

S

Yhat

weights

weighted moving average

 

1

67

 

 

 

 

 

2

63

63.78125

0.78125

0.4

25.2

25.2

3

70

60.5625

-9.4375

0.3

21

42

4

63

58.125

-4.875

0.2

12.6

37.8

5

59

46.25

-12.75

0.1

5.9

23.6

6

62

29.5

-32.5

 

0.647

3.235

 

 

 

 

 

 

131.835

 

 

 

 

 

EWMA

8.789

Period(t)

Sales(Y)

S

Yhat

weights

weighted moving average

 

1

67

 

 

 

 

 

2

63

58

-5

0.4

25.2

25.2

3

70

49

-21

0.3

21

42

4

63

35

-28

0.2

12.6

37.8

 

 

 

 

 

 

105

 

 

 

 

 

EWMA

17.5

We explored the advantage of a weighted moving average over a simple moving average; that advantage is the increased contribution, or influence, from the most recent data. We change the amount of influence by changing the length of the average interval, which in turn changes the weighting factors. We showed a 5-day weighted moving average that uses the values 5, 4, 3, 2, and 1 as the weighting factors. Thus, the most recent datum has 5 times the influence of the oldest datum. A 6 sales weighted moving average would give the most recent datum 10 times the influence of the oldest datum.

The exponential moving average (EMA) provides the same benefit by weighting ...