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| author | priyanka | 2015-06-24 15:03:17 +0530 |
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| committer | priyanka | 2015-06-24 15:03:17 +0530 |
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| tree | ab291cffc65280e58ac82470ba63fbcca7805165 /331/CH10/EX10.1 | |
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diff --git a/331/CH10/EX10.1/Example_10_1.sce b/331/CH10/EX10.1/Example_10_1.sce new file mode 100755 index 000000000..030f8e5bd --- /dev/null +++ b/331/CH10/EX10.1/Example_10_1.sce @@ -0,0 +1,75 @@ +//Caption:Correlation Analysis
+//Correlation Coefficient for Ungrouped Data (karl Pearson's Coefficient of Correlation)
+//The combination of hypotheses too test the significance of 'r' is as shown below:
+//Ho: r =0 (The two variables are not associated)
+//H1: r # 0 (The two variables are associated)
+//Example10.1
+//Page368
+clear;
+clc;
+X = [10,12,14,16,18,20,22,24,26,28];//Annual Advertising expenditure
+Y = [20,30,37,50,56,78,89,100,120,110];//Annual sales
+n = length(X);
+Xmean = mean(X);
+Ymean = mean(Y);
+disp(Xmean,'Mean of X=')
+disp(Ymean,'Mean of Y=')
+//correlation coefficient using basic formula
+r=0;
+num=0;
+den1=0;
+den2=0;
+for i = 1:n
+ num=num+((X(i)-Xmean)*(Y(i)-Ymean))
+ den1 = den1+(X(i)-Xmean)^2;
+ den2 = den2+(Y(i)-Ymean)^2;
+end
+r = num/(sqrt(den1)*sqrt(den2));
+disp(r,'The correlaion coefficient between annual advertising expenditure and annual sales revenue r =')
+//correlation coefficient using Pearson's product moment formula
+sumxi = sum(X);
+sumyi = sum(Y);
+xiyi = X.*Y;
+sumxiyi = sum(xiyi);
+sumxi2 = sum(X.^2);
+sumyi2 = sum(Y.^2);
+r = (n*sumxiyi-sumxi*sumyi)/(sqrt(n*sumxi2-sumxi^2)*sqrt(n*sumyi2-sumyi^2));
+disp(r,'The correlation coefficient using Pearsons product moment formula r=')
+t = r/sqrt((1-r^2)/(n-2));
+disp(t,'The calculated t statistic to test the significance of r t=')
+alpha = 0.05;
+alpha = alpha/2;
+t_stand = 2.306;
+disp(t_stand,'The table t value at half of the significance level and 8 degrees of freedom=')
+if (t<t_stand) then
+ disp('Since the calculated t statistic is less than table t value, accept Null hypothesis')
+else
+ disp('Since the calculated t statistic is greater than table t value, reject Null hypothesis')
+end
+//Result
+//Mean of X=
+//
+// 19.
+//
+// Mean of Y=
+//
+// 69.
+//
+// The correlaion coefficient between annual advertising expenditure and annual sales revenue r =
+//
+// 0.9851764
+//
+// The correlation coefficient using Pearsons product moment formula r=
+//
+// 0.9851764
+//
+// The calculated t statistic to test the significance of r t=
+//
+// 16.243604
+//
+// The table t value at half of the significance level and 8 degrees of freedom=
+//
+// 2.306
+//
+// Since the calculated t statistic is greater than table t value, reject Null hypothesis
+
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