Beachcomber Ltd in a local car dealership that sells used and new vehicles. The manager of the company wants to know how different variables affect the sales of his vehicles. A random sample of yearly data was taken with the view to testing the model: SALES=?+?AGE+?MIL+?ENG Where SALES= amount that a vehicle is sold for($000’s), AGE = age of the vehicle, MIL= the total mileage of the vehicle at the point of sale and ENG = the size of the engine. The sample of data was processed using MINITAB and the following is an extract of the output obtained: The regression equation is ***** Coef StDev t-ratio p-value Predictor Constant 1.7586 0.2525 6.9648 0.0000 AGE 0.2124 0.3175 * 0.5042 MIL -0.7527 0.3586 -2.0991 ** ENG 4.8124 0.6196 7.7664 0.0000 R-sq=56.1% R-sq(adj) =59.8% Analysis of Variance Source DF SS MS F p Regression 3 413.1291 138.7097 *** 0.00 Error 50 457.7607 2.2888 Total 53 a) What is dependent and independent variables? b) Fully write out the regression equation c) Fill in the missing values ‘*’, ‘**’, ‘***’and ‘***’. d) Hence test whether ? is significant. Give reasons for your answer. e) Perform the F Test making sure to state the null and alternative hypothesis. f) Given an interpretation of the term “R-sq” and comment on its value.
Beachcomber Ltd in a local car dealership that sells used and new vehicles. The manager of the
company wants to know how different variables affect the sales of his vehicles. A random sample of
yearly data was taken with the view to testing the model:
SALES=?+?AGE+?MIL+?ENG
Where SALES= amount that a vehicle is sold for($000’s), AGE = age of the vehicle, MIL= the total
mileage of the vehicle at the point of sale and ENG = the size of the engine. The sample of data was
processed using MINITAB and the following is an extract of the output obtained:
The regression equation is *****
Coef StDev t-ratio p-value
Predictor Constant 1.7586 0.2525 6.9648 0.0000
AGE 0.2124 0.3175 * 0.5042
MIL -0.7527 0.3586 -2.0991 **
ENG 4.8124 0.6196 7.7664 0.0000
R-sq=56.1% R-sq(adj) =59.8%
Analysis of Variance
Source DF SS MS F p
Regression 3 413.1291 138.7097 *** 0.00
Error 50 457.7607 2.2888
Total 53
a) What is dependent and independent variables?
b) Fully write out the regression equation
c) Fill in the missing values ‘*’, ‘**’, ‘***’and ‘***’.
d) Hence test whether ? is significant. Give reasons for your answer.
e) Perform the F Test making sure to state the null and alternative hypothesis.
f) Given an interpretation of the term “R-sq” and comment on its value.
Hi, thanks for the question. Since there are multiple subparts posted in the question, we will answer only the first three subparts. If you want any specific question to be answered, then submit that subpart only or mention the subpart number in the question.
a).
Here, the variable “SALES” is predicting by using the variables “AGE”, “MIL”, and “ENG”. Therefore, “SALES” is the dependent variable, and “AGE”, “MIL”, and “ENG” are independent variables.
b).
The regression model can be constructed by using the given output as follows:
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