Question

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5. For the following data set: ii) Calculater I iii) Use the Pearson Correlation Chart to determine ifr is significant using a = .05 and a = .01 0 3 13 6 13 9 5 17 21 # Hrs Playing Video Games, x GPA, y 4.00 3.58 2.9 3.00 2.7 2.20 3.58 1.50 1.00

Answer 1

Correlation coefficient

Pearson’s correlation coefficient is a statistical measure of the strength of a linear relationship between paired data. In a sample it is denoted by r and is by design constrained as follows

                       

-1<r<1

Furthermore:

· Positive values denote positive linear correlation;

· Negative values denote negative linear correlation;

· A value of 0 denotes no linear correlation;

· The closer the value is to 1 or –1, the stronger the linear correlation.

Pearson correlation coefficient value of -0.9252 i.e. there appears to be a negative correlation between the two variables.

To do this we test the null hypothesis, H0, that there is no correlation in the population against the alternative hypothesis, H1, that there is correlation; our data will indicate which of these opposing hypotheses is most likely to be true. We can thus express this test as:

                                    H0: r = 0

H1: r $\neq$ 0

i.e. the null hypothesis of no linear correlation present in population against the alternative that there is linear correlation present.

the p-value for this test as being .000 for both value of and thus we can say that we have very strong evidence to believe H1.

= 0.05 and 0.01

The significant Pearson correlation coefficient value of -0.9252 confirms what was apparent from the graph.

The value , the coefficient of determination is 0.856

R2

Scatterplot of Y vs X 4.0 3.5 3.0- 22.5 2.0 in 1.0 10 15 20 0 5 X