A regression equation has been developed in order to help predict the amount of sales made in a clothing store each day?(Y)?based on the number of square feet covered by the store's floor space?(X). A sample of 100 similar clothing stores is collected, with floor spaces ranging from 100 square feet to 300 square feet. For each store, the floor space (in square feet) and the amount of sales made that day (in dollars) are recorded. The following regression equation is calculated:
y^?= 2,035 + 58x
Select whether or not each of the following conclusions are correct from the regression analysis:
|a)||If the floor space of a store were to increase by one square foot, the predicted increase in sales would be $2,035.|
|b)||If a store has a floor space of 75 square feet, the predicted sales in a day is $6,385.|
|c)||If a store has a floor space of 175 square feet, the predicted sales in a day is $12,185.|
In simple linear regression, a common measure is the one given by the following formula:
Select the correct interpretation of what this formula means to the regression model:
|It is the amount of variation in the response variable that is accounted for by the explanatory variable.|
|It is the amount of variation in the explanatory variable that is not accounted for by the response variable.|
|It is the amount of variation in the response variable that is not accounted for by the explanatory variable.|
|It is the amount of variation in the explanatory variable that is accounted for by the response variable.|
A simple linear regression equation is to be constructed to determine if there is a linear relationship between a response variable?(Y)?and an explanatory variable?(X). A random sample of size n has been collected and the values xi?and yi?for?i = 1, 2, ..., n?have been recorded. The residuals?(ei)?in this analysis are defined as the difference between the observed values of Y and the values of Y predicted by the regression equation.
The scatterplot or residual plots can be used to see if the regression equation is an appropriate model for the data. An assumption required for the simple linear regression equation to be valid is:
|the variance of X is equal to the variance of Y|
|the residuals are independent of one another|
|X and Y are independent|
|the residuals are constant|
A regression equation has been developed in order to help predict the amount of sales made in a
clothing store each day (Y) based on the number of square feet covered by the store's floor
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