{"id":20225,"date":"2025-12-22T23:33:17","date_gmt":"2025-12-22T18:03:17","guid":{"rendered":"https:\/\/www.geographynotespdf.com\/?p=20225"},"modified":"2025-12-22T23:37:07","modified_gmt":"2025-12-22T18:07:07","slug":"correlation-analysis","status":"publish","type":"post","link":"https:\/\/geographynotespdf.com\/cms\/correlation-analysis\/","title":{"rendered":"14. Correlation analysis (\u0938\u0939\u0938\u0902\u092c\u0902\u0927 \u0935\u093f\u0936\u094d\u0932\u0947\u0937\u0923)"},"content":{"rendered":"

Correlation analysis<\/strong><\/span><\/h2>\n

(\u0938\u0939\u0938\u0902\u092c\u0902\u0927 \u0935\u093f\u0936\u094d\u0932\u0947\u0937\u0923)<\/strong><\/span><\/p>\n

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\u21d2 Correlation analysis deals with the association between two or more Variables.<\/span><\/strong><\/span><\/p>\n

\u21d2 The degree of relationship between the Variables Under consideration is measured through the correlation analysis.<\/span><\/strong><\/span><\/p>\n

\u21d2 The measure of correlation called the “Correlation coefficient or correlation index” Summarizes in Figure the direction & degree one of correlation.<\/span><\/strong><\/span><\/p>\n

Example1<\/strong><\/span><\/p>\n\n\n\n\n\n\n\n\n\n
x\u21d1<\/strong><\/span><\/td>\ny\u21d1<\/strong><\/span><\/td>\n<\/tr>\n
10<\/strong><\/span><\/td>\n15<\/strong><\/span><\/td>\n<\/tr>\n
12<\/strong><\/span><\/td>\n20<\/strong><\/span><\/td>\n<\/tr>\n
15<\/strong><\/span><\/td>\n22<\/strong><\/span><\/td>\n<\/tr>\n
18<\/strong><\/span><\/td>\n25<\/strong><\/span><\/td>\n<\/tr>\n
20<\/strong><\/span><\/td>\n37<\/strong><\/span><\/td>\n<\/tr>\n
25<\/strong><\/span><\/td>\n43<\/strong><\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n
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👉\u00a0 \u090a\u092a\u0930 \u0926\u093f\u090f \u0917\u090f \u0906\u0901\u0915\u0921\u093c\u094b\u0902 \u092e\u0947\u0902 x<\/strong> \u0914\u0930 y<\/strong> \u0915\u0947 \u092e\u093e\u0928\u094b\u0902 \u0915\u094b \u0926\u0947\u0916\u0928\u0947 \u092a\u0930 \u0938\u094d\u092a\u0937\u094d\u091f \u0939\u094b\u0924\u093e \u0939\u0948 \u0915\u093f \u091c\u0948\u0938\u0947-\u091c\u0948\u0938\u0947 x<\/strong> \u0915\u093e \u092e\u093e\u0928 \u092c\u0922\u093c\u0924\u093e \u0939\u0948, \u0935\u0948\u0938\u0947-\u0935\u0948\u0938\u0947 y<\/strong> \u0915\u093e \u092e\u093e\u0928 \u092d\u0940 \u092c\u0922\u093c \u0930\u0939\u093e \u0939\u0948\u0964<\/span><\/p>\n

👉\u00a0 \u0905\u0930\u094d\u0925\u093e\u0924\u094d, x \u092e\u0947\u0902 \u0935\u0943\u0926\u094d\u0927\u093f \u0939\u094b\u0928\u0947 \u092a\u0930 y \u092e\u0947\u0902 \u092d\u0940 \u0935\u0943\u0926\u094d\u0927\u093f \u0915\u0940 \u092a\u094d\u0930\u0935\u0943\u0924\u094d\u0924\u093f \u0926\u093f\u0916\u093e\u0908 \u0926\u0947\u0924\u0940 \u0939\u0948, \u091c\u093f\u0938\u0938\u0947 \u0926\u094b\u0928\u094b\u0902 \u091a\u0930 \u0906\u092a\u0938 \u092e\u0947\u0902 \u0938\u0915\u093e\u0930\u093e\u0924\u094d\u092e\u0915 \u0930\u0942\u092a \u0938\u0947 \u0938\u0902\u092c\u0902\u0927\u093f\u0924 \u0939\u0948\u0902\u0964<\/span><\/p>\n

👉 \u092f\u0939\u093e\u0901 x \u0914\u0930 y \u0915\u0947 \u092c\u0940\u091a \u0927\u0928\u093e\u0924\u094d\u092e\u0915 (Positive) \u0938\u0939\u0938\u0902\u092c\u0902\u0927<\/strong> \u0939\u0948\u0964<\/span><\/p>\n

Example2<\/strong><\/span><\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/article>\n<\/div>\n\n\n\n\n\n\n\n\n\n
x\u21d1<\/strong><\/span><\/td>\ny\u21d3<\/strong><\/span><\/td>\n<\/tr>\n
20<\/strong><\/span><\/td>\n40<\/strong><\/span><\/td>\n<\/tr>\n
30<\/strong><\/span><\/td>\n30<\/strong><\/span><\/td>\n<\/tr>\n
40<\/strong><\/span><\/td>\n22<\/strong><\/span><\/td>\n<\/tr>\n
50<\/strong><\/span><\/td>\n15<\/strong><\/span><\/td>\n<\/tr>\n
60<\/strong><\/span><\/td>\n10<\/strong><\/span><\/td>\n<\/tr>\n
80<\/strong><\/span><\/td>\n4<\/strong><\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

👉\u00a0 \u0926\u093f\u090f \u0917\u090f \u0906\u0901\u0915\u0921\u093c\u094b\u0902 \u092e\u0947\u0902 \u091c\u0948\u0938\u0947-\u091c\u0948\u0938\u0947 x \u0915\u093e \u092e\u093e\u0928 \u092c\u0922\u093c\u0924\u093e \u0939\u0948<\/strong>, \u0935\u0948\u0938\u0947-\u0935\u0948\u0938\u0947 y \u0915\u093e \u092e\u093e\u0928 \u0918\u091f\u0924\u093e \u091c\u093e\u0924\u093e \u0939\u0948<\/strong>\u0964<\/span><\/p>\n

👉\u00a0 \u0905\u0924\u0903 x \u0914\u0930 y \u0915\u0947 \u092c\u0940\u091a \u0928\u0915\u093e\u0930\u093e\u0924\u094d\u092e\u0915 (\u090b\u0923\u093e\u0924\u094d\u092e\u0915) \u0938\u0939\u0938\u0902\u092c\u0902\u0927<\/strong> \u092a\u093e\u092f\u093e \u091c\u093e\u0924\u093e \u0939\u0948\u0964<\/span><\/p>\n

👉\u00a0 \u091a\u0942\u0901\u0915\u093f \u092a\u0930\u093f\u0935\u0930\u094d\u0924\u0928 \u0928\u093f\u092f\u092e\u093f\u0924 \u0914\u0930 \u0938\u094d\u092a\u0937\u094d\u091f \u0939\u0948, \u0907\u0938\u0932\u093f\u090f \u092f\u0939 \u092a\u094d\u0930\u092c\u0932 \u0928\u0915\u093e\u0930\u093e\u0924\u094d\u092e\u0915 \u0938\u0939\u0938\u0902\u092c\u0902\u0927 (Strong Negative Correlation)<\/strong> \u0915\u094b \u0926\u0930\u094d\u0936\u093e\u0924\u093e \u0939\u0948\u0964<\/span><\/p>\n

Type of Correlation<\/strong><\/span><\/h3>\n

1. Positive Correlation (Direct Correlation):-<\/strong><\/span><\/p>\n

\u00a0 \u00a0If both the Variable in Same direction. x\u21d1, y\u21d1 or x\u21d3, y\u21d3 e.g., Height & Weight, Rainfall & Yeild<\/strong><\/span><\/p>\n

2. Negative Correlation <\/strong>(Inverse Correlation):-<\/strong><\/span><\/p>\n

\u00a0 \u00a0 If both the variables Varies in opposite direction. x\u21d1, y\u21d3 or x\u21d3, y\u21d1 e.g., Price & Demand<\/strong><\/span><\/p>\n

3. Zero Correlation (No Correlation):-<\/strong><\/span><\/p>\n

\u00a0 \u00a0 \u00a0 When there is no relationship between variables. or When one variable changes, the other variable does not change in any consistent way. x\u21d1\u21d3, y or x, y\u21d1\u21d3 e.g., Shoe size & intelligence<\/strong><\/span><\/p>\n

Correlation Coefficient (r)<\/strong><\/span><\/p>\n

\u00a0 \u00a0 \u00a0The correlation coefficient<\/strong> is a statistical measure that shows the strength and direction of the relationship between two variables. Its value ranges from \u22121 to +1, where positive values indicate direct correlation, negative values indicate inverse correlation, and zero indicates no relationship.<\/span><\/p>\n

r = +1 \u21d2 Perfect Positive Correlation,<\/strong><\/span><\/p>\n

r = -1 \u21d2 Perfect Negative Correlation,<\/strong><\/span><\/p>\n

r = 0 \u21d2 No Relation,<\/strong><\/span><\/p>\n

r = 0.8, 0.9, 0.95 \u0905\u0930\u094d\u0925\u093e\u0924 \u091c\u092c r \u0915\u093e Value 1 \u0915\u0947 \u0915\u0930\u0940\u092c \u0906\u0924\u093e \u0939\u0948 \u0924\u094b \u0909\u0938\u0947 Strong +ve Correlation \u0915\u0939\u093e \u091c\u093e\u0924\u093e \u0939\u0948\u0964<\/span><\/p>\n

r = -0.85, -0.9, -0.95 \u0905\u0930\u094d\u0925\u093e\u0924 \u091c\u092c r \u0915\u093e Value \u0932\u0917\u092d\u0917 -1 \u0915\u0947 \u0915\u0930\u0940\u092c \u0906\u0924\u093e \u0939\u0948 \u0924\u094b \u0909\u0938\u0947 Strong Negative Correlation \u0915\u0939\u093e \u091c\u093e\u0924\u093e \u0939\u0948\u0964<\/span><\/p>\n

Method of Finding Correlation Coefficient (r)<\/strong><\/span><\/p>\n

\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 The correlation coefficient (r) is found using several methods. The Karl Pearson\u2019s method<\/span><\/strong> is the most common, where r is calculated by dividing the covariance of two variables by the product of their standard deviations. <\/span><\/p>\n

\u00a0 \u00a0 \u00a0The Spearman\u2019s rank correlation method<\/span><\/strong> is used when data are ranked or not normally distributed. <\/span><\/p>\n

\u00a0 \u00a0 Another method is the concurrent deviations method<\/span><\/strong>, suitable for time-series data showing direction of change.<\/span><\/p>\n

\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0Scatter diagram method<\/strong><\/span> finds correlation coefficient (r) by plotting paired data points, observing pattern direction, and estimating strength visually.<\/span><\/p>\n

\u00a0 \u00a0These methods help measure the degree and direction of relationship between variables, with values of r ranging from \u20131 to +1.<\/span><\/p>\n

1. Karl Pearson\u2019s method<\/span><\/strong><\/p>\n

2. Spearman\u2019s rank correlation method<\/strong><\/span><\/p>\n

3. Concurrent deviations method<\/strong><\/span><\/p>\n

4. Scatter diagram method<\/strong><\/span><\/p>\n

1. Karl Pearson\u2019s Product Moment Method<\/strong><\/b><\/span><\/p>\n

\u00a0 \u00a0 \u00a0 Karl Pearson\u2019s Product Moment Method measures the degree and direction of linear relationship between two quantitative variables. It uses covariance divided by the product of their standard deviations, producing a correlation coefficient (r) ranging from \u20131 to +1, indicating negative, positive, or no correlation.<\/strong><\/span><\/p>\n

\"\"<\/span><\/p>\n

 <\/p>\n

Ex. (i) Find coefficient of correlation of the following data.<\/strong><\/span><\/p>\n\n\n\n\n\n\n\n\n\n\n\n\n
x<\/strong><\/span><\/td>\ny<\/strong><\/span><\/td>\n<\/tr>\n
9<\/strong><\/span><\/td>\n15<\/strong><\/span><\/td>\n<\/tr>\n
8<\/strong><\/span><\/td>\n16<\/strong><\/span><\/td>\n<\/tr>\n
7<\/strong><\/span><\/td>\n14<\/strong><\/span><\/td>\n<\/tr>\n
6<\/strong><\/span><\/td>\n13<\/strong><\/span><\/td>\n<\/tr>\n
5<\/strong><\/span><\/td>\n11<\/strong><\/span><\/td>\n<\/tr>\n
4<\/strong><\/span><\/td>\n12<\/strong><\/span><\/td>\n<\/tr>\n
3<\/strong><\/span><\/td>\n10<\/strong><\/span><\/td>\n<\/tr>\n
2<\/strong><\/span><\/td>\n8<\/strong><\/span><\/td>\n<\/tr>\n
1<\/strong><\/span><\/td>\n9<\/strong><\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

Solution:<\/strong><\/span><\/p>\n\n\n\n\n\n\n\n\n\n\n\n\n\n
x<\/strong><\/span><\/td>\ny<\/strong><\/span><\/td>\nx2<\/sup><\/strong><\/span><\/td>\ny2<\/sup><\/strong><\/span><\/td>\nxy<\/strong><\/span><\/td>\n<\/tr>\n
9<\/strong><\/span><\/td>\n15<\/strong><\/span><\/td>\n81<\/strong><\/span><\/td>\n225<\/strong><\/span><\/td>\n135<\/strong><\/span><\/td>\n<\/tr>\n
8<\/strong><\/span><\/td>\n16<\/strong><\/span><\/td>\n64<\/strong><\/span><\/td>\n256<\/strong><\/span><\/td>\n128<\/strong><\/span><\/td>\n<\/tr>\n
7<\/strong><\/span><\/td>\n14<\/strong><\/span><\/td>\n49<\/strong><\/span><\/td>\n196<\/strong><\/span><\/td>\n98<\/strong><\/span><\/td>\n<\/tr>\n
6<\/strong><\/span><\/td>\n13<\/strong><\/span><\/td>\n36<\/strong><\/span><\/td>\n169<\/strong><\/span><\/td>\n78<\/strong><\/span><\/td>\n<\/tr>\n
5<\/strong><\/span><\/td>\n11<\/strong><\/span><\/td>\n25<\/strong><\/span><\/td>\n121<\/strong><\/span><\/td>\n55<\/strong><\/span><\/td>\n<\/tr>\n
4<\/strong><\/span><\/td>\n12<\/strong><\/span><\/td>\n16<\/strong><\/span><\/td>\n144<\/strong><\/span><\/td>\n48<\/strong><\/span><\/td>\n<\/tr>\n
3<\/strong><\/span><\/td>\n10<\/strong><\/span><\/td>\n9<\/strong><\/span><\/td>\n100<\/strong><\/span><\/td>\n30<\/strong><\/span><\/td>\n<\/tr>\n
2<\/strong><\/span><\/td>\n8<\/strong><\/span><\/td>\n4<\/strong><\/span><\/td>\n64<\/strong><\/span><\/td>\n16<\/strong><\/span><\/td>\n<\/tr>\n
1<\/strong><\/span><\/td>\n9<\/strong><\/span><\/td>\n1<\/strong><\/span><\/td>\n81<\/strong><\/span><\/td>\n9<\/strong><\/span><\/td>\n<\/tr>\n
Total sum = 45<\/strong><\/span><\/td>\n108<\/strong><\/span><\/td>\n285<\/strong><\/span><\/td>\n1356<\/strong><\/span><\/td>\n597<\/strong><\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

n = No. of pair of observers<\/strong><\/span><\/p>\n

n = 9<\/strong><\/span><\/p>\n

\u03a3xy = 597<\/strong><\/span><\/p>\n

\u03a3x = 45<\/strong><\/span><\/p>\n

\u03a3y = 108<\/strong><\/span><\/p>\n

\u03a3x2 <\/sup>= 285<\/a><\/span><\/strong><\/span><\/p>\n

\u03a3y2<\/sup> = 1356<\/a><\/strong><\/span><\/p>\n

\"Correlation<\/span><\/p>\n","protected":false},"excerpt":{"rendered":"

Correlation analysis (\u0938\u0939\u0938\u0902\u092c\u0902\u0927 \u0935\u093f\u0936\u094d\u0932\u0947\u0937\u0923) \u21d2 Correlation analysis deals with the association between two or more Variables. \u21d2 The degree of relationship between the Variables Under consideration is measured through the correlation analysis. \u21d2 The measure of correlation called the “Correlation coefficient or correlation index” Summarizes in Figure the direction & degree one of correlation. 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