ISDS 200 Final Review Y dependent variable X1 X2 X3 ect independent variable s Example b0 5 b1 1 67 b2 10 15 Y 5 1 67X1 10 15X2 have to find P value if it statiscally significant If the P value for 1 67X1 is 0 15 If the P value for 10 15X2 is 0 32 Both P values have to be less than a alpha level of sig 01 05 10 for them to have a relationship P a RELATIONSHIP REJECT P a NO RELATIONSHIP DO NOT REJECT If P is less than whatever the given a is 01 05 10 RELATIONSHIP Example b1 1 67 P 04 Is there is a relationship between Y and X1 at 5 level Yes because P 05 R2 how much of a change in Y is caused by change in X variable s R2 coefficient of determination portion of the total variation in the dependent variable Y that is explained by variation in the independent variable X R2 1 perfect linear relationship between X and Y 100 of the variation in Y is explained by variation in X 0 R2 1 weaker linear relationships between X and Y some but not all of the variation in Y is explained by variation in X R2 0 no linear relationship between X and Y the value of Y does not depend on X none of the variation in Y is explained by variation in X Adjusted R2 only 1 Do not need Adj R2 if there is only 1 variable because Adj R2 R2 If you have more than 1 independent variable X1 X2 X3 ect and you want to compare 2 models use Adj R2 variable Example At 5 level of sig Y 5 10X1 7X2 R2 82 Adj R2 81 this is the answer because Adj R2 is greater Y 12 7X1 8X2 92X3 R2 86 Adj R2 79 Overall significance H0 B1 B2 Bk 0 no linear H1 at least one Bk 0 at least 1 of the independent variable X affects Y relationship Overall test of regression H0 B1 0 no linear relationship H1 B1 0 linear relationship does not Test for b1 parameter exist H0 B2 0 H1 B2 0 Test for b2 parameter b0 is the estimated average value of Y when the value of X is zero b1 is the estimated change in the average value of Y as a result of a one unit increase X SSE error sum of squares Sb1 estimate of the standard error of the slope SYX standard error of the slope K of independent variables X