Question

Problem Definition:

A wholesale supplier wants to predict the average cost associated with shipping orders of various sizes. The order sizes and shipping costs for the past twelve months are provided in the table below. Set alpha at .01.

Order sizes and shipping costs for last twelve months

Size of Orders =X	Shipping Costs =Y
1068	4489
1026	5611
767	3290
885	4113
1156	4883
1146	5425
892	4414
938	5506
769	3346
677	3673
1174	6542
1009	5088

Review the analysis example provided to become familiar with Minitab commands and statistical testing needed to complete the analysis of shipping costs.

Enter the data shown above regarding shipping costs and sizes of orders into Minitab

Create Sections for Each of the Following. Grading will based upon strict adherence to this format and proper testing techniques.

Problem Definition (why are you doing this analysis/)

Begin with Problem Definition

Scatterplot

Use Minitab Scatterplot with description of relationship between x and y. Describe scatterplot to determine whether positive or negative and explain how you made this determination in your graph description? Neither?

Correlation Coefficient

Hypothesis test of correlation coefficient to determine if a linear relationship exists between Size or Order and Shipping Cost– Use six step process

Use OLS (ordinary least squares as demonstrated during lecture and as shown in this handout. Be sure to select expanded tables under the Results dialog box.

Regression Equation (show only the equation not the entire table or output)

Use Minitab to develop the regression equation-In your report, paste the Minitab output of regression equation and define regression coefficients b₀ and b₁ as learned during lecture.

bo = and is defined as…

b1= and is defined as….

Be able to discuss the quantitative assessment of each in terms of order cost.

Significance Testing (ANOVA) What percentage of error or variation is …

F Test to test R-sqd – Use six step process and in interpretation step discusses percentage of variability in y explained by x. Use six step process

Significance Testing (Regression Coefficient) Is x a significant predictor of y?

T test for significance of regression coefficient Use six step process in interpretation step discuss average amount of change in y for one unit change in x.

Satisfying Regression Assumptions (Normality and Homoscedasticity)

Minitab plots to include in report: Size graphs to fit neatly within report and place each description with the graph you are discussing. Graphical analyses are used to evaluate residuals plotted on graphs. Each graph speaks to one or more of the regression assumptions that are used to determine if the model is valid and may be used for prediction and/or net regression analysis

Regression Plots and associated assumptions

-NP Plot for residuals -Minitab graph with description addressing to assumption(s)

-Residuals vs. Fits-Minitab graph with description addressing to assumption(s)

-Residuals and x variable-Minitab graph with description addressing to assumption(s)

Confidence Interval for Regression Coefficient

Develop confidence interval for regression coefficient and interpret – Minitab 18 of calculates confidence intervals about the regression coefficient b_k are computed when the expanded table selection is chosen under the Results command box.

Prediction and Confidence Interval for Fit value of Y

Use Minitab to develop prediction interval and confidence interval for y for a value of x you select and enter into Minitab – Be able to interpret both intervals as they relate to y for given values of x

Answer 1

Problem Definition (why are you doing this analysis/)

We want to predict the average shipping cost for orders for various size

Scatterplot

Graph -> scatterplot -> simple

Scatterplot: Simple Worksheet 1 *** C1 х cix c2y X variables Y variables y 1 C12 013 014 1 C2 у 4489 5611 3290 2 1068 1026 767 885 1156 1146 892 938 Scale... Labels... Data View... Multiple Graphs... Data Options... 4113 4883 5425 4414 5506 3346 3673 6542 Select 9 769 677 Help ок | 10 11 Cancel 1174

click ok

Scatterplot of y vs x 7000 6000 > 5000 4000 3000 700 700 800 900 900 1000 1100 1100 1200 1200 X

There seems to be positive correlation as generally when x increases, y increases.

Correlation Coefficient

stat -> basic stat -> correlation

Correlation: x, y

C3 C4 C5 Correlation C6 C1 x | C2 y Variables: Worksheet 1 *** C1 х 1068 1026 767 885 1156 1146 892 938 769 677 1174 C2 у 4489 5611 3290 4113 4883 5425 4414 5506 3346 3673 6542 Method: Pearson correlation - Display p-values Select Store matrix (display nothing) Help Help OK Cancel Cancel -O... O O X Sca. Ou

Pearson correlation of x and y = 0.820
P-Value = 0.001

Ho:p=0

Ha :P +0

n - 2 t = r 1 - p2

= 4.52

p-value = 0.001

since p-value < alpha

we reject the null hypothesis

we conclude that there is significant correlaiton

r = 0.820

Use OLS (ordinary least squares as demonstrated during lecture and as shown in this handout.
Be sure to select expanded tables under the Results dialog box.

STAT -> regression -> regression -> fit regression model

сіх C2 y Responses: 03 04 Continuous predictors: Worksheet 1 *** 01 х 1068 1026 767 885 1156 1146 892 938 769 677 1174 02 y 4489 5611 3290 4113 4883 5425 4414 5506 3346 3673 6542 Categorical predictors: 9 10 Model... 11 Model. Coding... Options... | Coding... stepwise Select Graphs... Results... Storage

click on results to get explanded table in display of results

Regression Analysis: y versus x Analysis of Variance Source Regression DF Seg ss Contribution 1 7340820 67.17% 1 7340820 67.17% 10 3588357 32.83% 11 10929177 100.00% Adj SS Adj MS 7340820 7340820 7340820 7340820 3588357 358836 F-Value 20.46 20.46 P-value 0.001 0.001 Error Total Model Summary S R-sq 599.029 67.17% R-sq(adj) PRESS R-sq (pred) 63.88% 5252213 51.94% Coefficients Coef VIF Term Constant Coef SE Coef -31 1060 4.93 1.09 95% CI (-2393, 2330) ( 2.50, 7.36) T-Value -0.03 4.52 P-Value 0.977 0.001 1.00 Regression Equation y = -31 + 4.93 x

y^ = -31 + 4.93 *x

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