Predicting annual home-furnishing sales
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Assignment two
An analyst sought to predict the annual sales for a home-furnishing manufacturer using the following predictor variables:
X1=marriage during the year
X2=housing starts during the year
X3=annual disposable personal income
X4=time trend (first year=1, second year=2, and so forth)
Using data for 24 year, the analyst calculated the following estimating equation:
Y=49.85-0.068x1+0.036x2+1.22x3-19.54x4
The analyst also calculated an R2=0.92 and a standard error of estimate of 11.9
The value of R2 helps in determining how well a linear model fits the data. It tells how close the data is to the regression line. The value of R2 Whether low or high cannot be termed as good or bad (Brown & Vaughn, 2011). However, generally, when the value of R2 is high it implies that the model fits the data well. In this case, a value of 0.92 is high meaning the model fit the data well. When the value of R2 is 0%, the implication is the model shows no variability of the response data in relation to the mean. When R2 is 100%, the model explains the entire variability of the data in relation to the mean (Nonaka, 2012).
R-squared has limitations, as it cannot determine if there is bias in its coefficient estimates and predictions. The residual points must therefore be assed. The adequacy of a regression model cannot be indicated using R-squared whether it is high or low. A low R-squared values are not inherently bad or good (Bhatti, Rehman & Zaheer, 2011). For instance, when using R-squared to predict human behavior as in psychology, the value of R-squared is usually low and less than 50% because of the difficulty in predicting human behavior compared to physical processes (Buzzetto-More, 2012).
Regarding the standard error of estimate, when the value is small for a regression line, the prediction is more accurate. In the above case where the standard error of estimate is 11.9, it may not produce a prediction interval of 95%, which is regarded as sufficiently narrow. The standard error of estimate should be 2.5 or less. The model therefore needs to be more precise. The analyst need to consider other factors affecting the sales of furniture such as other competitor industries in order to come up with a better estimating equation that can give higher value of R-squared and lower value of standard error of estimate (Conole, 2010).