Question

Management of Erudition, an online learning platform, is keen to motivate students to work hard. In order to quantify the degree of effort put in by each learner, the company has decided to collect data on the amount of time spent by students on their virtual learning environ- ment and the grades obtained by them. The following data have been collected.

Develop a regression equation expressing grades as a function of the amount of time spent on the online learning platform.

Student Groups Grades (%) Time Spent (hours)
1 20 0
2 25 15
3 40 25
4 50 35
5 55 45
6 60 65
7 65 80
8 70 95
9 75 100

Answer 1

To find the regression equation relating grades to time spent on an online learning platform, calculate the slope and intercept using means, covariance, and variance of the given data points, then formulate the equation.

Step-by-step explanation:

To determine the linear regression equation, which predicts grades based on the time spent on the online learning platform, we can use the given data points. The regression equation has the form: y = mx + b, where y is the predicted grade, m is the slope, x is the time spent, and b is the y-intercept.

By utilizing the least squares method, we calculate the slope (m) as the covariance of the grades and time spent divided by the variance of the time spent. The intercept (b) is calculated as the mean of the grades minus the product of the slope and the mean of the time spent.

Step-By-Step Calculation:

1. Calculate the mean of the grades and the mean of the time spent.
2. Compute the covariance between grades and time.
3. Calculate the variance of the time spent.
4. Determine the slope (m) using the covariance and variance.
5. Find the intercept (b) using the means and the slope.
6. Formulate the equation: Grade = m * Time Spent + b.

Once we have calculated m and b, we substitute these values into the regression equation to predict student grades based on their time spent on the online learning platform.