You look at the relationship between how much time people spend on the website ‘Bookface’ and how productive they are at work.
time spent on Bookface is the predictor variable, and time spent working is the response variable.
correlation between minutes spent on Bookface and minutes spent working is -0.5.
The standard deviation in Bookface time is 4.86, and the standard deviation of time spent working is 3.50.
You want to find the values for the equation ŷi=a+bxi. What is the value of the slope?
I worked the equation as the the
following -
-0.5(4.86/3.50) - 1.38857 but I got this wrong I wanted to know where in the formula I had went wrong for future learning. As I am lost about the equation and the slope
Can anyone help explain this to me.
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.
Well, it seems like you're trying to calculate the slope for the equation ŷi=a+bxi, given the correlation between time spent on Bookface and time spent working. Let me break it down for you:
In this case, the correlation coefficient (r) between Bookface time and working time is -0.5. The formula for calculating the slope (b) from the correlation coefficient is:
b = r * (standard deviation of y / standard deviation of x)
In your case, y represents time spent working and x represents time spent on Bookface. The standard deviation of y is 3.50, and the standard deviation of x is 4.86.
So, plugging in the values:
b = -0.5 * (4.86 / 3.50)
b = -0.5 * 1.38857
b = -0.694285
Therefore, the value of the slope (b) is approximately -0.694285.
To find the value of the slope (b) in the equation ŷi = a + bxi, you need to use the correlation coefficient and the standard deviations of the predictor and response variables.
The correlation coefficient (r) measures the strength and direction of the linear relationship between the two variables. In this case, the correlation between minutes spent on Bookface and minutes spent working is -0.5.
The standard deviation of Bookface time is 4.86, and the standard deviation of time spent working is 3.50.
The formula for the slope (b) can be calculated as follows:
b = r * (standard deviation of response variable / standard deviation of predictor variable)
Using the given values, we have:
b = -0.5 * (3.50 / 4.86)
b = -0.5 * 0.7194
b ≈ -0.3597 (rounded to four decimal places)
So, the value of the slope (b) in the equation is approximately -0.3597.
To find the value of the slope (b) in the equation ŷi = a + bxi, you need to use the formula for the correlation coefficient (r) and the standard deviations of the two variables.
The formula to calculate the slope when you have the correlation coefficient is:
b = r * (σy / σx)
Where:
- b is the slope
- r is the correlation coefficient
- σy is the standard deviation of the response variable (time spent working)
- σx is the standard deviation of the predictor variable (time spent on Bookface)
In your case, the correlation coefficient (r) is given as -0.5, the standard deviation of time spent on Bookface (σx) is 4.86, and the standard deviation of time spent working (σy) is 3.50.
Now let's plug in the values into the formula:
b = -0.5 * (4.86 / 3.50)
b = -0.5 * 1.38857
b = -0.694285
So, the value of the slope (b) is approximately -0.694285.
It appears that you made a mistake in your calculation. The negative sign (-) should be moved outside of the parentheses, multiplying both the correlation coefficient and the ratio of standard deviations.
Remember to double-check your calculations and ensure that all values are properly accounted for to avoid errors in the future.