All Greens is a franchise store that sells house plants and lawn and garden supplies. Although All Greens is a franchise, each store is owned and managed by private Sh individuals. Some friends have asked you to go into business with them to open a new All Greens store in the suburbs of San Diego. The national franchise headquarters sent 8. you the following information at your request. These data are about 27 All Greens stores in California. Each of the 27 stores has been doing very well, and you would like to use the information to help set up your own new store. The variables for which we have data are detailed below. X1 = annual net sales, in thousands of dollars = number of square feet of floor display in store, in thousands of square feet X2 = value of store inventory, in thousands of dollars Sh 1.1 Хз X4 = amount spent on local advertising, in thousands of dollars X5 = size of sales district, in thousands of families X6 = number of competing or similar stores in sales district A sales district was defined to be the region within a 5 mile radius of an All Greens store. X2 Xз 294 X4 X5 8.2 231 3 8.2 11 156 2.2 232 6.9 4.1 12 10 0.5 149 3 4.3 15 519 5.5 600 12 16.1 Sh 7.5 437 4.4 567 10.6 14.1 487 4.8 571 11.8 12.7 4 299 3.1 512 8.1 10.1 10 195 2.5 347 7.7 8.4 12 20 1.2 212 3.3 2.1 15 68 0.6 102 4.9 4.7 570 5.4 788 17.4 12.3 1 Sh 3.5 428 4.2 577 10.5 14.0 464 4.7 535 11.3 15.0 3 15 0.6 163 2.5 2.5 14 65 1.2 168 4.7 3.3 11 98 1.6 151 4.6 2.7 10 398 4.3 342 5.5 16.0 4 161 2.6 196 7.2 6.3 13 Sh 9.3 397 3.8 453 10.4 13.9 497 5.3 518 11.5 16.3 528 12.3 615 278 16.0 6.5 5.6 99 0.8 2.8 14 0.5 1.1 142 3.1 1.6 12 347 3.6 461 9.6 11.3 341 3.5 382 9.8 11.5 5 Бh 6.0 507 5.1 590 12.0 15.7 400 8.6 517 7.0 12.0 8.
Correlation
Correlation defines a relationship between two independent variables. It tells the degree to which variables move in relation to each other. When two sets of data are related to each other, there is a correlation between them.
Linear Correlation
A correlation is used to determine the relationships between numerical and categorical variables. In other words, it is an indicator of how things are connected to one another. The correlation analysis is the study of how variables are related.
Regression Analysis
Regression analysis is a statistical method in which it estimates the relationship between a dependent variable and one or more independent variable. In simple terms dependent variable is called as outcome variable and independent variable is called as predictors. Regression analysis is one of the methods to find the trends in data. The independent variable used in Regression analysis is named Predictor variable. It offers data of an associated dependent variable regarding a particular outcome.
(c) Perform a
%
(d) Write out the regression equation. (Use 2 decimal places for x3 and x6. Use 1 decimal place otherwise.)
| x1 = | + x2 | + x3 | + x4 | + x5 | + x6 |
If 11 new competing stores moved into the sales district but the other explanatory variables did not change, what would you expect for the corresponding change in annual net sales? (Use 2 decimal places.)
If you increased the local advertising by 8 thousand dollars but the other explanatory variables did not change, what would you expect for the corresponding change in annual net sales? (Use 2 decimal places.)
(e) Test each coefficient to determine if it is or is not zero. Use a 5% level of significance. (Use 2 decimal places for t and 3 decimal places for the P-value.)
| t | P-value | |
| β2 | ||
| β3 | ||
| β4 | ||
| β5 | ||
| β6 |
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