A researcher measures the relationship between internet use (hours per week) and

Question

A researcher measures the relationship between internet use (hours per week) and social interaction (hours per week) in a sample of 10 students. The following table lists the hypothetical results of this study.
Internet Use (X) 6 7 6 7 13 5 4 5 2 12
Social Interaction (Y) 3 5 7 6 4 6 3 5 9 3
A) Compute the Pearson correlation coefficient. (Round your answer to three decimal places.)
B) Compute the coefficient of determination. (Round your answer to three decimal places.)
C) Using a two-tailed test at a 0.05 level of significance, state the decision to retain or reject the null hypothesis.
A researcher measures the relationship between internet use (hours per week) and social interaction (hours per week) in a sample of 10 students. The following table lists the hypothetical results of this study.
Internet Use (X) 6 7 6 7 13 5 4 5 2 12
Social Interaction (Y) 3 5 7 6 4 6 3 5 9 3
A) Compute the Pearson correlation coefficient. (Round your answer to three decimal places.)
B) Compute the coefficient of determination. (Round your answer to three decimal places.)
C) Using a two-tailed test at a 0.05 level of significance, state the decision to retain or reject the null hypothesis.
A researcher measures the relationship between internet use (hours per week) and social interaction (hours per week) in a sample of 10 students. The following table lists the hypothetical results of this study.
Internet Use (X) 6 7 6 7 13 5 4 5 2 12
Social Interaction (Y) 3 5 7 6 4 6 3 5 9 3
A) Compute the Pearson correlation coefficient. (Round your answer to three decimal places.)
B) Compute the coefficient of determination. (Round your answer to three decimal places.)
C) Using a two-tailed test at a 0.05 level of significance, state the decision to retain or reject the null hypothesis.

Explanation / Answer

Using R

X=c(6,7,6,7,13,5,4,5,2,12)
Y=c(3,5,7,6,4,6,3,5,9,3)

A) Compute the Pearson correlation coefficient. (Round your answer to three decimal places.)

> cor(X,Y)
[1] -0.5259218

Pearson correlation coefficient = -0.525

b) Compute the coefficient of determination. (Round your answer to three decimal places.)

> model=lm(Y~X)
> R2=summary(model)$r.squared
> R2
[1] 0.2765938

coefficient of determination = 0.276

C) Using a two-tailed test at a 0.05 level of significance, state the decision to retain or reject the null hypothesis.

> summary(model)

Call:

lm(formula = Y ~ X)

Residuals:

Min 1Q Median 3Q Max

-2.9222 -0.5848 0.1868 0.9481 2.4688

Coefficients:

Estimate Std. Error t value Pr(>|t|)   

(Intercept) 7.1402 1.2948 5.515 0.000564 ***

X -0.3045 0.1741 -1.749 0.118423   

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Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 1.776 on 8 degrees of freedom

Multiple R-squared: 0.2766, Adjusted R-squared: 0.1862

F-statistic: 3.059 on 1 and 8 DF, p-value: 0.1184

Comment= You can see above P-value =0.118423 which is greater than 0.05 so We fail to Reject null hypothesis.

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