Question: a) Prepare a scatter plot of the data. Based on your plot, does a simp
ID: 3171876 • Letter: Q
Question
Question:
a) Prepare a scatter plot of the data. Based on your plot, does a simple linear regression model appear adequate for modelling the sales data?
b) Use the Box-Cox procedure and standardization discussed in class to find an appropriate power transformation of Y . Evaluate SSE for = 0.2, 0.1, 0, 1, 2. What transformation of Y is suggested?
c) Apply the transformation Y = log_10Y to the data and analyze the data using SLR analysis.
d) Plot the estimated regression line and the transformed data. Does the regression line appear to be a good fit to the transformed data?
e) Obtain the residuals and plot them against the fitted values. Also prepare a Q-Q plot. What do your plots show?
f) Express the estimated regression function for the transformed data in the original units.
Show all the workings and R-studio codes.
Data:
Explanation / Answer
scatter plot of the data
Regression Analysis: Y versus X
The regression equation is
Y = 2.58 - 0.324 X
Predictor Coef SE Coef T P
Constant 2.5753 0.2487 10.35 0.000
X -0.32400 0.04330 -7.48 0.000
S = 0.474314 R-Sq = 81.2% R-Sq(adj) = 79.7%
Analysis of Variance
Source DF SS MS F P
Regression 1 12.597 12.597 55.99 0.000
Residual Error 13 2.925 0.225
Total 14 15.522
After Transformation of Log Y
MTB > let C4 = log(Y)
MTB > Name c5 "RESI2"
MTB > Regress 'LnY' 1 'X';
SUBC> Residuals 'RESI2';
SUBC> Constant;
SUBC> Brief 1.
Regression Analysis: LnY versus X
The regression equation is
LnY = 1.51 - 0.450 X
Predictor Coef SE Coef T P
Constant 1.50792 0.06028 25.01 0.000
X -0.44993 0.01049 -42.87 0.000
S = 0.114956 R-Sq = 99.3% R-Sq(adj) = 99.2%
Analysis of Variance
Source DF SS MS F P
Regression 1 24.292 24.292 1838.23 0.000
Residual Error 13 0.172 0.013
Total 14 24.464
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