I am confused I want to find the values of the equation of Yi=a + bxi.
Time spent on twitter is the predictor variable and time spent working on twitter is the response
The correlation between minutes spent on twitter and minutes spent working is -0.5
The standard deviation in Twitter time is 4.86 and the standard deviation of time spent working is 3.50
I tried the following -0.5(4.86/3.50) or 4.86/3.50*-0.5 but not sure if correct way. Any one help explain this to me please.
To find the values of the equation Yi = a + bxi, where Yi represents the time spent working on Twitter and xi represents the time spent on Twitter, you need to use the formula for the linear regression model.
The correlation coefficient (r) between minutes spent on Twitter and minutes spent working is -0.5. This value indicates the strength and direction of the linear relationship between the two variables.
To find the slope (b) of the equation, you can multiply the correlation coefficient (r) by the standard deviation of the response variable (Y) divided by the standard deviation of the predictor variable (x). In this case, you would calculate:
b = r * (standard deviation of Y) / (standard deviation of x)
In your case, the standard deviation of Twitter time (x) is 4.86 and the standard deviation of time spent working (Y) is 3.50. Plugging these values into the equation, you would have:
b = -0.5 * (4.86 / 3.50)
To find the intercept (a) of the equation, you can use the formula:
a = mean(Y) - b * mean(x)
Where mean(Y) is the mean of the response variable (time spent working) and mean(x) is the mean of the predictor variable (time spent on Twitter).
Overall, the steps to find the values of the equation Yi=a + bxi would be:
1. Calculate the slope (b) using the formula: b = r * (standard deviation of Y) / (standard deviation of x).
2. Calculate the mean of the response variable (mean(Y)) and the mean of the predictor variable (mean(x)).
3. Calculate the intercept (a) using the formula: a = mean(Y) - b * mean(x).
By following these steps, you can find the values of a and b and determine the equation Yi = a + bxi for the given data.