Question

1. The following data represent the homework grades and current course grades for fifteen students. Is there a correlation between homewosk and the course at a 1% level significance?

1. The following data represent the homework grades and current course grades for fifteen students. Is there a correlation between homework grades and grades in the course at a 1% level of significance? Homework Grade Current Course Grade 56 65 69 (a) What are the null and alternative lıypotheses? (b) What is the correlation coefficient? (Round to two decimal places.) (c) What is the p-value? (Round to four decimal places.) (d) Is there sufficient evidence to reject the mull hypothesis? Explain (e) What is the conclusion? (1) If there is a correlation, state the equation for the line of Least-Squares. (Round coefficients to three decimal places.) (6) The process of predicting inside of the observed values is called interpolation. Find the predicted current course grade if the student has a homework grade of 67. (h) The process of predicting outside of the observed x values is called extrapolation. Find the predicted current course grade if the student has a homework grade of 100.

Answer 1

G H 1 Homework Grade Current Course Grade SUMMARY OUTPUT Regression Statistics Multiple R 0.748563827 R Square 0.560347803 Adjusted R Square 0.526528403 Standard Error 12.89630915 Observations ANOVA Regression Residual Total 1 13 14 SS MS F Significance F 2755.641067 2755.641 16.56883 0.001324453 2162.092266 166.3148 4917.733333 Intercept Homework Grade Coefficients Standard Error Stat P-value Lower 95% 14.19194403 15.03375185 0.944005 0.362382 -18.2865022 0.846049943 0.20785004 4.070482 0.001324 0.397017232 Upper 95% 46.67039031 1.295082654

a) $H_0: \rho =0$

$H_a: \rho \neq 0$

b) The correlation coefficient is r = 0.75

c) Test statistic : $t=r\sqrt{\frac{n-2}{1-r^2}}=0.75\sqrt{\frac{15-2}{1-0.56}}=4.077$

degree of freedom= n-2=13

P value for two tailed test is = 0.0013

d)Since theP value is less than the significance level 0.01, we shall reject the null hypothesis.

e)The test is significant we have evidence that there is a significant correlation between the two variable.

f) line of Least Squares is Y = 14.192+0.846X