Suppose UWG is deciding whether or not to build a new library. It costs money to

Question

Suppose UWG is deciding whether or not to build a new library. It costs money to support a building

and other libraries' amounts depend on square footage as shown here:

Area

x Cost in thousands y

25 310

40 300

45 420

55 410

60 460

(a) Calculate the mean and standard deviations of the data. Use Excel.

(b) Calculate the correlation coecient. Use Excel.

(c) Calculate the slope and intercept of the regression line. Write down the equation of the line. (Do

not use Excel for this part).

(d) Verify your answer for part (c) by using Data

! Data Analysis ! Regression in Excel

(e) What hypothesis would you test about the slope of the line? Do two-sided.

(f) Calculate the standard deviation of the regression. To do this, you will need to construct the

residuals by hand, so you will need to make a prediction using your line for all ve data points

and will need to square those residuals and add them together.

(g) Calculate a test statistic, and compare to a critical value of your choice.

(h) Construct a prediction interval for an individual value of

y and a condence interval for a mean

value of

y when the area is 35.

Explanation / Answer

Correlation

r( X,Y) =    Co V ( X,Y) / S.D (X) * S.D (y)                      
r( X,Y) =    Sum(XY) / N- Mean of (X) * Mean of (Y) / Sqrt( X^2/n - ( Mean of X)^2 ) Sqrt( Y^2/n - ( Mean of Y)^2 )                        
                          
Co v ( X, Y ) =   1 /5 (88800) - [ 1/5 *225 ] [ 1/5 *1900] =            660          
S. D ( X ) =   Sqrt( 1/5*10875-(1/5*225)^2)           12.247          
S .D (Y) =    Sqrt( 1/5*742200-(1/5*1900)^2)           63.561          
r(x,y) =    660 / 12.247*63.561   =   0.8479              
                          
If r = 0.8479> 0 ,Perfect Positive Correlation                          

[ANSWERS]

a. Mean of x = 225/5 = 45, S.D (X) = 12.247

Mean of y = 1900/5 = 480, S.D(Y) = 63.561

b.

correlation(r) = 0.8479

c.

Line of Regression Y on X i.e Y = bo + b1 X

Mean of X = X / n =    45
Mean of Y = Y / n =   380
(Xi - Mean)^2 =   750
(Yi - Mean)^2 =   20200
(Xi-Mean)*(Yi-Mean) =   3300
b1 = (Xi-Mean)*(Yi-Mean) / (Xi - Mean)^2    
b1 = 3300 / 750 = 4.4  
bo = Y / n - b1 * X / n  
bo = 380 - 4.4*45 = 182  
  
Y = bo + b1 X  
  
Y'=182+4.4*X  

slope(b1) = 4.4

d. EXCEL OUTPUT

Note: As - per chegg, experts - only - solve - 4- sub parts - in - a - question -per -thread. Please -ask -the -remaining -in -different- post

( X) ( Y) X^2 Y^2 X*Y 25 310 625 96100 7750 40 300 1600 90000 12000 45 420 2025 176400 18900 55 410 3025 168100 22550 60 460 3600 211600 27600 225 1900 10875 742200 88800 Totals

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