Paper Topic:

Correlation and Regression Problem (Elem Stats)

Correlation and Regression Activity

Part I : Correlation

Don 't forget to state the ed pair you used (28 , 84

a ) State the value of the correlation coefficient

Value of the correlation coefficient R SQRT (0 .7569 0 .87

b ) Is it significant at the 5 level , 1 level , both levels , or neither level (You should consult Table I on page 738 of the textbook

df 9-2 7 ? 0

Level of Significance (p ) for Two-Tailed Test

at the 5 level (CV -0 .666

at the 1 level (CV -0 .798 0

at the 95 level of confidence 0 at the 99 level of confidence

Therefore , there is a significant linear relationship between the messages written and the expected score on a final exam at the 5 level and 1 level i .e . at both levels exists

c ) Write a conclusion in the context of this problem

There is a strong positive (0 .87 is closer to 1 ) correlation (linear relationship ) between the on a final exam exists

Part II : Regression

Note : do this part of the activity even if r was not significant at the 5 level for Step b of Part I above , so that you will have the practice and feedback to your posting in to help you with the Term Project and the Final Exam

d ) State the slope and then state its meaning in the context of this problem

y 1 .3943x 51 .127

In above regression equation the coefficient of x represents the slope of the equation

Slope 1 .394

The slope represents the marginal change in dependent variable (y ) if change is made on independent variable (x . In this case , it means that for each additional message written by a student we expect the score on the final exam to increase by 1 .394 (rounded 1 .4 ) points

e ) State the coefficient of determination ant then state its meaning in the context of this problem

The coefficient of determination

R^2 0 .7569 75 .69

The result means that 75 .69 of the variation in the dependent variable (final exam scores ) is accounted for by the variations in the independent variable The coefficient of non-determination is in this case is 24 .31 . This is the unexplained portion of the variation between the two variables...

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