Standard Error

Question

Determine SSE, SS (Total) and the explained sum of squared variation SSR, as well as the standard error and the coefficient of correlation for the data:
 

An experiment was performed on a certain metal to determine if the strength is a function of heating time. Results based on 10 metal sheets are given below. Use the simple linear regression model.
∑X = 30
∑X2 = 104
∑Y = 40
∑Y2 = 178
∑XY = 134

Question

     A suburban hotel derives its gross income from its hotel   and restaurant operations. The owners are interested in the relationship   between the number of rooms occupied on a nightly basis and the revenue per   day in the restaurant. Below is a sample of 25 days (Monday through Thursday)   from last year showing the restaurant income and number of rooms occupied.   

Day    Income    Occupied   1     $1,452          23   2      1,361          47   3      1,426          21   4      1,470          39   5      1,456          37   6      1,430          29   7      1,354       23   8      1,442       44   9      1,394          45   10    1,459          16   11     1,399          30   12     1,458          42   13     1,537       54   14     $1,425       27   15    1,445          34   16     1,439       15   17      1,348       19   18     1,450       38   19      1,431      4   20      1,446      47   21      1,485      43   22      1,405       38   23      1,461       51   24      1,490       61   25      1,426      39    

     a)Does the   breakfast revenue seem to increase as the number of occupied rooms increases? Draw a scatter diagram to support your conclusion.    

     b)Determine the coefficient of correlation between the two variables. Interpret the value.    

     c)Is it   reasonable to conclude that there is a positive relationship between revenue and occupied rooms? Use the .10 significance level.    

     d)What percent of the variation in revenue in the restaurant is accounted for by the number of rooms occupied?