Applebee's International, Inc., is a U.S. company that...

Applebee's International, Inc., is a U.S. company that develops, franchises, and operates the Applebee's Neighborhood Grill and Bar restaurant chain. It is the largest chain of casual dining restaurants in the country, with over 1,500 restaurants across the United States. The headquarters is located in Overland Park, Kansas. The company is interested in determining if mean weekly revenue differs among three restaurants in a particular city. The file entitled Applebees contains revenue data for a sample of weeks for each of the three locations. a. Test to determine if blocking the week on which the testing was done was necessary. Use a significance level of 0.05 . b. Based on the data gathered by Applebee's, can it be concluded that there is a difference in the average revenue among the three restaurants? c. If you did conclude that there was a difference in the average revenue, use Fisher's LSD approach to determine which restaurant has the lowest mean sales.

Applebee's International, Inc., is a U.S. company that develops, franchises, and operates the Applebee's Neighborhood Grill and Bar restaurant chain. It is the largest chain of casual dining restaurants in the country, with over 1,500 restaurants across the United States. The headquarters is located in Overland Park, Kansas. The company is interested in determining if mean weekly revenue differs among three restaurants in a particular city. The file entitled Applebees contains revenue data for a sample of weeks for each of the three locations.
a. Test to determine if blocking the week on which the testing was done was necessary. Use a significance level of 0.05 .
b. Based on the data gathered by Applebee's, can it be concluded that there is a difference in the average revenue among the three restaurants?
c. If you did conclude that there was a difference in the average revenue, use Fisher's LSD approach to determine which restaurant has the lowest mean sales.

Key Concepts

Hypothesis Testing

Hypothesis testing involves making statistical decisions about a population parameter through the evaluation of sample data. In this context, it includes formulating a null hypothesis (e.g., no difference in means among groups) and an alternative hypothesis (e.g., a difference exists), setting a significance level (such as 0.05), and then using test statistics to decide whether to reject the null hypothesis.

Fisher's Least Significant Difference (LSD)

Fisher's LSD is a post-hoc test used after a statistically significant ANOVA result to conduct pairwise comparisons between group means. It determines the minimum difference required for the means to be considered statistically different, allowing researchers to identify exactly which groups differ from each other while controlling for the overall error rate.

Blocking

Blocking is an experimental design strategy that involves grouping experimental units that are similar with respect to certain nuisance variables. This approach controls for potential confounding factors by ensuring that comparisons among the main treatments are made within these relatively homogenous blocks, thereby increasing the accuracy and precision of the estimated treatment effects.

Analysis of Variance (ANOVA)

ANOVA is a statistical method used to test for differences among group means by decomposing the overall variability observed in the data into variability attributable to different sources. In comparing multiple groups, it helps determine whether at least one group mean is significantly different from the others, forming the basis for further pairwise comparisons if needed.

Transcript

00:01 So we have the sales and the income for this situation, and we're told to let the independent variable be the income and the sales be y, and that would be a common mistake for people to make because they list the sales first that people will think that that's the independent variable.

00:18 But we have our means for the two variables, and then we can find the sum of squared for each of these, and then the sum of squares for the x, x.

00:30 Y and i have those listed in my columns just have to add them up and so we'll go to second in list and sum of the first one ends up being the 1 ,146 .4 for the second one we have the sum of the sum of 696 and for that last sum of squares we have the sum of have a sum of 782 now we're asked to find the regression equation for this line and so i'm going to on part b i just use my lin reg of a plus b x on list one and list two and so stat calculate and that happens to be number eight in my value and we end up getting that the predicted y value, which again is our sales, and that sales is in thousands of dollars, and we have the income is also in thousands of dollars.

01:51 We have a negative 2 .198 plus 0 .6821 .x.

02:00 X and then it says briefly explain the values calculated in part b this tells us that if the if the income is zero then we would expect the sales to be negative 2 .198 in thousands or negative 2 ,198 which again doesn't make sense for our slow as the income rises by one in thousands we expect the sales to go up and that would end up up being 682 .1 because it's 0 .6821 in thousands.

03:00 Next we're asked to calculate in part d we want to look at what r and r squared would be and we know we can find our r value by taking our sum of squares of x y divided by the square root of the sum of squares of xx x times the sum of squares of the y however i'm going to just use my software to find that and that is 0 .875 the r squared value i'm going to list as a is 76 .64%.

03:38 And this tells us that there is a strong, relatively strong, positive association between our two variables.

03:52 And this tells us that around 77 % of the variation in our sales is explained.

04:03 Is explained by this model.

04:12 And then you want for part e, you want the standard deviation for the air, and that value comes out to be, if we do a lin -regg t test, that will give it to us...

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