According to a survey, as reported by The Guardian in 2014, more students now work to fund their studies. In order to see whether students' long working hours affect their studies, a social scientist...

According to a survey, as reported by The Guardian in 2014, more students now work to fund their studies.  In order to see whether students' long working hours affect their studies, a social scientist estimate a linear regression to examine the relationship between the number of weekly hours worked (x) by the students and the marks obtained (y) by them in Statistics subject.  The excel output of the linear regression is reproduced below:

1. The relationship between the variable x and y is Answer,


2. The values of the intercept and slope coefficients are Answer,


3. The least square line from the above output is Answer,


4. The value of the coefficient of determination  is Answer,


5. Select appropriate interpretation for slope coefficient: Answer,


6. Calculate the coefficient of correlation and type your answer in this box (round it up to 4 decimal places):  = Answer

In order to determine whether there is enough evidence to conclude that a linear relationship exists between the variable y and variable x we perform hypothesis testing at 5 percent significance level.  Answer the following questions:

1. The null hypothesis is H0:β1 Answer,


2. The alternative hypothesis is H1:β1 Answer,


3. As per excel output, the value of t-statistic for this test is Answer,


4. The decision rule is to reject H0 if Answer,


5. Given the observed value of the test statistic, we decide to Answer.

Extracted text: SUMMARY OUTPUT Regression Statistics Multiple R 0.9290 RSquare Adjusted RSquare 0.8631 0.8494 Standard Error 7.2278 Observations 12 ANOVA df MS Significance F SS F Regression Residual 1.0000 3,292.2546 3,292.2546 63.0203 0.0000 10.0000 522.4121 52.2412 Total 11.0000 3,814.6667 Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Intercept 92.7904 4.0034 23.1778 0.0000 83.8702 101.7105 Hours Worked -1.4029 0.1767 -7.9385 0.0000 -1.7967 -1.0092