Question

The coefficient of linear correlation between the sales and the number of employees is found to be r=-0.66. Which of the following values cannot be the slope of the line of the linear regression? -2.7 . -1.8 -1.9 1.5

Answer 1

Q1) As the correlation coefficient here is -0.66 which is less than 0, therefore the slope also has to be negative as the sign of correlation coefficient should be same as the sign of slope. Therefore 1.5 cannot be the value of the slope coefficient here as it is positive.

Q2) The given data is inputted in EXCEL and the SCATTERPLOT was obtained. Using the TRENDLINE function, we obtain the regression equation along with the correlation coefficient. Therefore the scatter plot here is obtained as:

у y = 0.3875x -0.1563 R = 0.528 23 20 15 10 5 0 o 10 20 30 40 50 60

a) The coefficient of correlation here is computed as:

$r = \sqrt{R^2} = \sqrt{0.528} = 0.73$

b) The intercept of the regression equation as can be seen from the above plot is -0.16
Therefore -0.16 is the intercept here.

c) The slope here in similar way is given as 0.39. Therefore 0.39 is the slope of the regression equation here.

Q3) As the p-value here is 0.034 < 0.05 which is the level of significance, therefore the test is significant here and we can reject the null hypothesis here. Therefore there is sufficient evidence here to conclude that judges employed by the Federal court in Abu Dhabi have an average salaro more than 50,000 AED. Therefore B is the correct answer here.