Question

The Tasty Sub Shop Case:

A business entrepreneur uses simple linear regression analysis to predict the yearly revenue for a potential restaurant site on the basis of the number of residents living near the site. The entrepreneur then uses the prediction to assess the profitability of the potential restaurant site.

And

The QHIC Case:

The marketing department at Quality Home Improvement Center (QHIC) uses simple linear regression analysis to predict home upkeep expenditure on the basis of home value. Predictions of home upkeep expenditures are used to help determine which homes should be sent advertising brochures promoting QHIC’s products and services.

Discuss the difference in the type of prediction in both cases and provide rational of the reasons that these predictions were used.

Answer 1

Answer:-

Given That:-

The Tasty Sub Shop Case:

A business entrepreneur uses simple linear regression analysis to predict the yearly revenue for a potential restaurant site on the basis of the number of residents living near the site. The entrepreneur then uses the prediction to assess the profitability of the potential restaurant site.

And

The QHIC Case:

The marketing department at Quality Home Improvement Center (QHIC) uses simple linear regression analysis to predict home upkeep expenditure on the basis of home value. Predictions of home upkeep expenditures are used to help determine which homes should be sent advertising brochures promoting QHIC’s products and services.

This is a simple problem related to analysis of the difference in the regression models for two cases .

To analyse it we need to firstly understand the models .

In the tasty sub shop case, a simple linear regression equation is used to plot the response variable ( Revenue -Y ) with the help of predictor variable (number of residents living in close by area-X) .This is simple we will have a simple linear equation as below

Y =β0+β1X+ξ , Where β0=constant intercept , β1=slope or rate of change of the revenue with a unit change in number of residents and ξ =error factor

Now clearly the above expression is directly and only dependent on the variation of X (number of residents living in close by area-X) .

The revenue figure is in turn is used to calculate the profitability.

P =Revenue -cost

Thus we can get a direct prediction of the profitability from the number of residents

Now what is the quality of the prediction?

The prediction is direct and not inferential .

Now lets look at the QHIC case .In this case, a simple linear regression equation is used to plot the response variable ( home upkeep expenditure -Y ) with the help of predictor variable (Home value-X) .This is simple we will have a simple linear equation as below

Y =β0+β1X+ξ , Where β0=constant intercept , β1=slope or rate of change of the expenditure with a unit change in home value and ξ =error factor

Now clearly the above expression is directly and only dependent on the variation of X (Home value-X) .

The revenue figure is in turn is used to take decision on advertisement segment to target.

Clearly, this is not a direct relation . We can develop a scale to filter the home segments for advertisements.

This is an indirect inference.

Thus we cant get a direct prediction

Now what is the quality of the prediction?

The prediction is indirect and not pin pointed. It will thus have large variation in the overall outcome variable ( predictor variable – houses for advertisement ) since it not only depend on only one variable (home value) but also on choice of scale for