Question

CH 10 Correlation and regression

1) All these pages after filled boxes (part e)

Sugar Consumption X 2.1 5 6.3 6.5 7.7 8.7 11.6 Cavities    Y 0.59 1.51 1.55 1.7 2.18 2.1 2.73

a. Enter the above data into an excel spreadsheet.

b. Use the CORREL function and find the Linear Correlation Coefficient r (five decimal digits) and write in box below

Linear Correlation Coefficient r =  

c. Use the Regression dialog box and find the regression equation

d. Fill out the boxes below


Regression Equation:

Using your regression equation above how many cavities would you expect a child in this age range to have if they consumed 13.0 kg of sugar annually?

Answer 1

( b )

Using CORREL function in Excel we get

Linear Correlation Coefficient r = 0.97905

( c )

Using Regression in Excel we get output as

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.979049237
R Square	0.958537408
Adjusted R Square	0.95024489
Standard Error	0.149958042
Observations	7
ANOVA
	df	SS	MS	F	Significance F
Regression	1	2.599334357	2.599334	115.5906	0.00012066
Residual	5	0.112437072	0.022487
Total	6	2.711771429
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%
Intercept	0.251974611	0.151776025	1.660174	0.157773	-0.13817808	0.642127303
X	0.221214566	0.020575595	10.75131	0.000121	0.168323315	0.274105818

From the above output

• Regression equation is

y = 0.2519746 + 0.2212146 x

• given x = 13

then

y = 0.2519746 + 0.2212146 ( 13 )

= 3.1277644

y = 3.1277644