Project #2 - Alexa Stockover Stats Project #2 810-83-0687...

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Alexa Stockover 810-83-0687 Sec 206 Stats Project #2 In the scatter plot below, data from a national restaurant chain is compared to determine whether the square of a restaurant has an influence on the annual revenue earned from the restaurant. The explanatory variable, represented by the variable x, is the square footage per restaurant. The response variable, represented by the variable y, is the annual revenue per square foot. The results of the scatter plot show that there is a weak, negative relationship between the two variables relationship is moderately weak. This means that as the square footage of a restaurant increases, the annual revenue of the restaurant decreases. (12.32) The linear model, y = -.182x + 889.364, is not very credible because there is not a very strong correlation throughout the data. (12.33) The slope of the linear model means that for every additional square foot added to the restaurant, the restaurant will lose $.182 in annual sales per square foot. The intercept of the model does not have any meaning because it means that when the size of the restaurant is zero square feet, they would earn $889.36 for each square foot, which does not make logical sense given the range of the data. (12.34) After examining the results for the regression analysis, the regression model proves to be a poor fit. The coefficient of determination, or R², compares SSR (regression sum of squares) with SSE (error sum of squares) to tell the relative fit of the model. The closer to one the value of R² is, the better the fit. The closer to zero R² is, the poorer the fit. The R² value of the given data from the restaurants is .247 which is close to zero showing that the regression model is a poor fit for the data. (12.37a) Another way to measure the fit of the regression model is through the use of the F statistic and the p-value. The F statistic uses the sample size and the ratio SSR to SSE to
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Project #2 - Alexa Stockover Stats Project #2 810-83-0687...

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