The issues concerning the application and interpretation of regression analysis
ID: 3274809 • Letter: T
Question
The issues concerning the application and interpretation of regression analysis have been discusses in chapter four (multiple regression analysis) by following the six-stage model-building framework(Stage 1: Objectives of Multiple Regression, Stage 2: Research Design of Multiple Regression, Stage 3: Assumptions in Multiple Regression Analysis, Stage 4: Estimating the Regression Model and Assessing Overall Fit,Stage 5: Interpreting the Regression VariateStage 6: Validation of the Results)
For this assignment, you will provide an illustration of the important questions at each stage by considering the application of multiple regression analysis to a research problem specified by HBAT. Consider a research setting in which HBAT has obtained a number of measures in a survey of customers. To demonstrate the use of multiple linear regression, show the procedures used by researchers to attempt to predict customer satisfaction (X19) of the individuals in the sample with a set of 16 independent variables (X3 to X18). Use the SPSS data set HBAT_200.sav.
the dataset file is uploaded here:- http://ge.tt/77xCmZm2
Explanation / Answer
Solution:
Here, we have to discuss six stage multiple regression building framework for the given data by using SPSS. We have to discuss all six stages regarding HBAT dataset.
Stage 1
The objective of this multiple regression model is to estimate or infer about the dependent or response variable Satisfaction based on the several independent variables or predictors.
Stage 2
Research design used for this data is multiple linear regression model. The variables from X3 to X18 are independent variables or predictors while the variable X18 (satisfaction) is the dependent or response variable.
Stage 3
Assumptions:
We assume that the population data for the given variables follows approximate normal distribution and all pairs of independent variables do not have any significant linear relationship. There should be absence of autocorrelation for significance of the multiple regression model.
Stage 4
Estimation of regression model:
The SPSS output for this regression model is given as below:
Model Summary
Model
R
R Square
Adjusted R Square
Std. Error of the Estimate
1
.918a
.842
.829
.5136
a. Predictors: (Constant), X18 - Delivery Speed, X4 - Region, X8 - Technical Support, X15 - New Products, X7 - E-Commerce, X5 - Distribution System, X3 - Firm Size, X10 - Advertising, X6 - Product Quality, X13 - Competitive Pricing, X16 - Order & Billing, X17 - Price Flexibility, X14 - Warranty & Claims, X12 - Salesforce Image, X9 - Complaint Resolution, X11 - Product Line
ANOVAb
Model
Sum of Squares
df
Mean Square
F
Sig.
1
Regression
258.258
16
16.141
61.180
.000a
Residual
48.281
183
.264
Total
306.539
199
a. Predictors: (Constant), X18 - Delivery Speed, X4 - Region, X8 - Technical Support, X15 - New Products, X7 - E-Commerce, X5 - Distribution System, X3 - Firm Size, X10 - Advertising, X6 - Product Quality, X13 - Competitive Pricing, X16 - Order & Billing, X17 - Price Flexibility, X14 - Warranty & Claims, X12 - Salesforce Image, X9 - Complaint Resolution, X11 - Product Line
b. Dependent Variable: X19 - Satisfaction
Coefficientsa
Model
Unstandardized Coefficients
Standardized Coefficients
t
Sig.
B
Std. Error
Beta
1
(Constant)
-1.807
.719
-2.514
.013
X3 - Firm Size
.512
.093
.207
5.490
.000
X4 - Region
-.257
.126
-.102
-2.033
.043
X5 - Distribution System
.414
.094
.167
4.387
.000
X6 - Product Quality
.354
.036
.395
9.869
.000
X7 - E-Commerce
-.236
.081
-.146
-2.911
.004
X8 - Technical Support
-.011
.042
-.015
-.261
.794
X9 - Complaint Resolution
.129
.066
.126
1.949
.053
X10 - Advertising
-.017
.043
-.016
-.392
.695
X11 - Product Line
.324
.169
.344
1.923
.056
X12 - Salesforce Image
.519
.068
.472
7.642
.000
X13 - Competitive Pricing
-.054
.031
-.068
-1.714
.088
X14 - Warranty & Claims
.086
.083
.061
1.037
.301
X15 - New Products
.055
.026
.066
2.131
.034
X16 - Order & Billing
.045
.067
.033
.667
.506
X17 - Price Flexibility
.285
.176
.274
1.622
.107
X18 - Delivery Speed
-.137
.340
-.083
-.403
.687
a. Dependent Variable: X19 - Satisfaction
Stage 5
Interpretation:
The multiple correlation coefficient is given as 0.918 which indicate strong linear relationship between dependent variable satisfaction and other independent variables. The coefficient of determination or the value of R square is given as 0.842, which means about 84.2% of the variation in the dependent variable satisfaction is explained by the independent variables. For the above multiple regression model, the p-value for the ANOVA table is given as 0.00 which indicate that the given regression model is statistically significant and we can use this multiple regression model for further estimation. The variables like technical support, advertising , warranty and claims, order and billing, price flexibility and delivery speed are statistically not significant.
Stage 6
Validity of results
Although given regression model is statistically significant, but there are some coefficients or independent variables which are not statistically significant. For more effective regression model, we need to eliminate these non-significant variables from the multiple regression model.
Model Summary
Model
R
R Square
Adjusted R Square
Std. Error of the Estimate
1
.918a
.842
.829
.5136
a. Predictors: (Constant), X18 - Delivery Speed, X4 - Region, X8 - Technical Support, X15 - New Products, X7 - E-Commerce, X5 - Distribution System, X3 - Firm Size, X10 - Advertising, X6 - Product Quality, X13 - Competitive Pricing, X16 - Order & Billing, X17 - Price Flexibility, X14 - Warranty & Claims, X12 - Salesforce Image, X9 - Complaint Resolution, X11 - Product Line
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