Question

It is thought that basketball teams that make too many fouls in a game tend to lose the game even if they otherwise play well. Let x be the number of fouls more than (i.e., over and above) the opposing team. Let y be the percentage of times the team with the larger number of fouls wins the game. х 33 26 y48 44 14, Ey 151, x2 = 66, Ey2 = 6005, Exy Complete parts (a) through (e), given Ex 457, and r -0.993. (a) Draw a scatter diagram displaying the data Get ADOBP FLASH PLAYER Flash Player version 10 or higher is required for this question You can get Flash Player free from Adobe's website (b) Verify the given sums Ex, Xy, Ex2, Zy2, ^xy, and the value of the sample correlation coefficient r. (Round your value for r to three decimal places.) Σχ - Σy - Еху %3D r = (c) Find x, and y. Then find the equation of the least-squares line y a + bx. (Round your answers for x and y to two decimal places. Round your answers for a and b to three decimal places.) y

Answer 1

F G H I J K L M N O P TV 2 Nm 2304 1936 1089 676 165 156 457 26 151 37.75 14 6005 00 9 Correlation 12 Y -0.99336699 SW 15 SUMMARY OUTPUT x Line Fit Plot 17 Regression Statistics 18 MultipleR 0.99336699 19 R Square 0.986777976 20 Adjusted RSC 0.980166964 21 Standard Errc 1.419403354 22 Observations 1 2 3 4 5 6 7 24 ANOVA oy Predicted y 1 26 Regression 27 Residual 28 Total MS F Significance F 300.7205882 300.72059 149.26277 0.006633 4 .029411765 2.0147059 304.75 2 3 Intercept Coefficients 52.47058824 -4.205882353 Standard Error Stat P-value L ower 95% Upper 95% Lower 95.0% Upper 95.0% 1.398373994 37.522572 0.0007095 46.453871 58.487306 46.453871 58.487306 0.34425588 -12.217315 0.006633 -5.6870959 -2.7246689 -5.6870959 -2.7246689 86 RESIDUAL OUTPUT Predicted value for x = 4 x=4 35.647059 Observation Predictedy R esiduals 1 48.26470588 -0.264705882 2 44.05882353 -0.058823529 3 31.44117647 1.558823529 4 27.23529412 -1.235294118

All analysis is done in Microsoft Excel '

A) scatter plot of data is shown above . It can be obtained by using inserting plot in Excel

B)

Values are verified and evaluated values are highlighted in orange colour

Value of correlation can be obtained by using correlation tool of Excel

Steps to do correlation anlaysis

go to data tab -> data analysis -> correlation-> select the range of x and y -> click okay

similarly we can do Regression analysis using same toolpak

C)

$\bar{X}$ = 3.5

Y = 37.75

Y = 52.47 – 4.205X

D) as we can see the plot in the output look similar to that of plot given in option A

as the intercept is 52.47 and it is the only plot with intercept given above.

E)

r² = 0.98677

which implies that

% of variation explained = 98.677

% unexplained variation = 100 - 98.677 = 1.323

F)

for x = 4 we can easily get the predicted value of y by the regression (least squares ) equation given above by putting x = 4

* = 52.47- 4.205 x 4 = 35.647059