Inspect the preceding scatter diagram and the regression analysis output for num
ID: 3125620 • Letter: I
Question
Inspect the preceding scatter diagram and the regression analysis output for number of customers versus number of items purchased. Look for evidence that either supports or contradicts the claim, “There is a linear relationship between the two variables.” a. Describe the graphical evidence found and discuss how it shows lack of linearity for the entire range of values. Which ordered pairs appear to be different from the others? b. Describe how the numerical evidence shown indicates that the linear model does fit this data. Explain. c. Some of the evidence seems to indicate the linear model is the correct model, and some evidence indicates the opposite. What months provided the points that are separate from the rest of the pattern? What is going on in those months that might cause this?
Regression Analysis: Items versus Customers The regression equation is Items =-154 + 3.56 Customers Predictor Coef Constant Customers 3.5591 0.1284 27.71 s= 405.075 R-Sq=92.8% R-Sa(adj)=92.6% SE Coef T 153.6 108.2 -1.420.161 0.000Explanation / Answer
a) From the graph, points are scattered around the line and the line is in the upward direction. Therefore, it is a positive linear correlation.
However, few points are deviated from the line [at( x=1200-1600,y=5000-6000) and (x=2500 ,y=7000]. So, linearity lacks at these range of values.
b) Given:
The regression equation is
Items=-154+3.56Customers
It is in the form Y=a+bX, which is linear.
The coefficients a=-154, b=3.56 are estimated by ‘method of least square’.
So, the numerical evidence indicates that the linear model does fit this data.
C) Few points are deviated from the line.
Also, a=-154, -ve and SE coeff=108.2.
Based on these evidences, linear model does not fit at some cases.
This occurs when both the values ‘Items’ and ‘customers’ are high. Precisely, when ‘the demand’ of the item is more.