The objective of a study is to produce a multiple regression model to predict sales of cotton xplanatory variables are

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Question-1: The objective of a study is to produce a multiple regression model to predict sales of cotton
fabric. The explanatory variables are
X,
Whole sale price index
Quantity of Imported Fabric
х,
Quantity of Exported Fabric
x.
Time
Part of a computer output from the estimated regression based on 28 observations is shown below:
Predictor
Constant
Coeff StdDev
8876
2295
X,
-24
25
-6
2.5
X,
0.5
0.2
63
70
Analysis of Variance
Source
Regression
Error
SS
21080
1426
22506
Total
a) Write down the estimated regression equation and interpretthe estimated regression coefficients
for X, and X3.
b) Suppose we drop the variable 14 from the model. The reduced regression model has XI , X2 and
13 as explanatory variables. The reduced model has R? = 0.9. Test if the reduced regression model
is significant or not at significance level 0.05.
c) Suppose you believe that the quantity of cotton fabric sold may also be impacted by how cold the
weather is. Furthermore, suppose you have classified the weather in three categories, cold, normal,
warm. Design a regression model that allows for the new variables and show how you test your
hypothesis.
Transcribed Image Text:Question-1: The objective of a study is to produce a multiple regression model to predict sales of cotton fabric. The explanatory variables are X, Whole sale price index Quantity of Imported Fabric х, Quantity of Exported Fabric x. Time Part of a computer output from the estimated regression based on 28 observations is shown below: Predictor Constant Coeff StdDev 8876 2295 X, -24 25 -6 2.5 X, 0.5 0.2 63 70 Analysis of Variance Source Regression Error SS 21080 1426 22506 Total a) Write down the estimated regression equation and interpretthe estimated regression coefficients for X, and X3. b) Suppose we drop the variable 14 from the model. The reduced regression model has XI , X2 and 13 as explanatory variables. The reduced model has R? = 0.9. Test if the reduced regression model is significant or not at significance level 0.05. c) Suppose you believe that the quantity of cotton fabric sold may also be impacted by how cold the weather is. Furthermore, suppose you have classified the weather in three categories, cold, normal, warm. Design a regression model that allows for the new variables and show how you test your hypothesis.
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