A company which markets and repairs small computers needs to forecast the number
ID: 3297095 • Letter: A
Question
A company which markets and repairs small computers needs to forecast the number of service engineers required over the next few years. This requires consideration of the length of service calls, which in turn depends on the number of components that need to be repaired or replaced. The data given below consists of the number of components repaired and the length of the service call (in minutes) for a random sample of 24 calls. We will use a simple regression model to explain the relationship between the length of service call (response variable, Y ) and the number of repaired units (predictor variable, X). (a) Make a scatterplot (with a regression line) of Y versus X. Present the least-squares line for predicting Y from X. (b) Plot the residuals versus the fitted values. Does the model seem appropriate? (c) Now, consider a multiple linear regression model to fit the data with X and X2 as predictors. Compare R2 ’s from SLR and MLR. (d) Plot the residuals versus the fitted values. Which model seems more appropriate?
Data:
X Y 1 23 2 29 3 49 4 64 4 74 5 87 6 96 6 97 7 109 8 119 9 149 9 145 10 154 10 166 11 162 11 174 12 180 12 176 14 179 16 193 17 193 18 195 18 198 20 205Explanation / Answer
(a) Here the independent variable is X and dependent Variable is Y
Regression Analysis: Y versus X
The regression equation is
Y = 37.2 + 9.97 X
Predictor Coef SE Coef T P
Constant 37.213 7.985 4.66 0.000
X 9.9695 0.7218 13.81 0.000
S = 18.7534 R-Sq = 89.7% R-Sq(adj) = 89.2%
According to regression analysis the least square line for explaining Y from X is Y = 37.2 + 9.97 X and since coeficient of X is 9.97 we can say there is no any other dependant factors while X is change by one unit Y may change by 9.97.
b)
According to the graph the residual vs fitted value it seems to have curved relationship between Residual Vs fitted value but to appropriate the model there should be uncorelated. Hence can say that by considering the Residual Vs fitted value there plot the model is not appropriate.
c)
Regression Analysis: Y versus X, X2
The regression equation is
Y = - 9.75 + 22.2 X - 0.589 X2
Predictor Coef SE Coef T P
Constant -9.753 4.865 -2.00 0.058
X 22.226 1.051 21.14 0.000
X2 -0.58857 0.04888 -12.04 0.000
S = 6.82723 R-Sq = 98.7% R-Sq(adj) = 98.6%
In SLR R2 (R-Sq) 89.7% is equal to 89.2% and in MLR R2 (R-Sq) 98.7% hence in SL 89.7% of Y can be explained by X variable and in ML 98.6% of Y can be explained by using both X and X2. Comparatively ML is more appropriate than SL when R2 ( R-Sq) is considered.
d)
It seems to be don't have any corelation with residual vs Fitted Value graph the model is consider to be appropriate to explain the data by using ML (Multiple Regression).
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