Question

Explain whether there are any correlations that suggest the problem of multicollinearity. Why or why not? Use at least two examples from your correlation matrix as part of your explanation. Number of bedrooms Correlations Number of Square feet of bathrooms finished living (fractions) space 551" .637" Number of floors .278" Lot size (square feet) .132" .000 796 Building Condition .049 .171 Building Grade .376" Year built 233" Number of bedrooms 1 .000 .000 .000 .000 .000 796 796 796 796 .551" 796 .711" 796 .618 796 .544" 1 .026 Number of bathrooms (fractions) .562" .030 .000 .000 458 000 405 796 796 Pearson Correlation Sig. (2-tailed) N Pearson Correlation Sig. (2-tailed) N Pearson Correlation Sig. (2-tailed) N Pearson Correlation Sig. (2-tailed) N 796 .637" 796 .711" 796 420" 796 097" .000 796 .698 .000 796 .296 SR 1 Square feet of finished living space 250" .000 .000 .000 .000 006 .000 .000 796 796 796 796 .026 796 .250" 796 --091 Lot size (square feet) 1 -.084 796 --006 866 796 .132" .000 796 278" .149 458 .000 018 .000 010 796 796 796 796 562 796 .420 796 - 104" 796 .481" Number of floors Pearson Correlation - 084 1 420 .000 .000 .000 .018 .003 .000 .000 796 796 796 796 796 796 .097" 796 - 104" Building Condition 049 030 -006 1 047 Sig. (2-tailed) N Pearson Correlation Sig, (2-tailed) N Pearson Correlation Sig. (2-tailed) 796 -.1939 .000 796 .405 796 .618" .006 796 .866 796 .003 796 .181 796 796 Building Grade .698" 149" 481" .047 1 475" .171 796 .376" .000 796 233" .000 .000 .000 000 .000 .181 .000 796 796 796 544" 796 .296" 796 - 091 Year built 796 420" .000 N Pearson Correlation Sig. (2-tailed) N 1 796 .475" .000 - 193" .000 .000 .010 .000 796 796 796 796 796 796 796 796 ** Correlation is significant at the 0.01 level (2-tailed). * Correlation is significant at the 0.05 level (2-tailed).

Please help in solving this.

Answer 1

Multicollinearity refers to a situation in which two or more explanatory variables in a multiple regression model are highly linearly related and can be linearly predicted from the others with a substantial degree of accuracy.

So, we look for variables that are correlated with each other.

Yes there are correlations that suggest the problem of multicollinearity.

Examples:

• Consider no. of bedrooms and its correlation with no. of bathrooms (fraction) = 0.551 and square ft of finished living space = 0.637. Now here, both the variables no. of bathrooms and square ft of finished living space are themselves correlated with correlation 0.711.

All these three correlations are significant at 0.01

Now what happens is there is some amount of variability explained in no. of bedrooms by no. of bathrooms(fraction) and then there is some varaibility explained by square ft of finished living space. The problem is since they both are correlated they explain variability in each other too. If we consider both to study variation in no. of bedrooms then we end up counting the same variation twice.

Similarly, another example is :

• Square feet of finished living space with building grade and year built have significant correlation of 0.698 and 0.296 respectively where both building grade and year built have significant correlation of 0.475.

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