I am confused by the following and need some help
You want to find the values for the equation ŷi=a+bxi. What is the value of the slope?
time spent on Bookface predictor variable,
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.
Would the formula be something like the following
Yi=4.86+3.50-0.5 = 7.86 I am not sure if I am working this out as the answer is wrong I just would like to know where I went wrong for future learning points.
To find the value of the slope (b) in the equation ŷi=a+bxi, you need more information than just the correlation and standard deviations. The correlation (-0.5) only tells you the direction and strength of the linear relationship between the two variables (minutes spent on Bookface and minutes spent working). It does not give you the value of the slope.
To find the slope, you would need to calculate the covariance between the two variables (Bookface time and time spent working) and divide it by the variance of the predictor variable (Bookface time). The formula for the slope (b) is:
b = Cov(x, y) / Var(x)
Where Cov(x, y) is the covariance between the two variables (Bookface time and time spent working) and Var(x) is the variance of the predictor variable (Bookface time).
Without the actual data, it is not possible to determine the slope value. The formula you provided in your example, ŷi = 4.86 + 3.50 - 0.5, does not correctly calculate the slope.
To find the value of the slope in the equation ŷi = a + bxi, we need to use the given information about the correlation between the predictor variable (time spent on Bookface) and the response variable (time spent working).
The correlation coefficient (r) represents the strength and direction of the linear relationship between two variables. In this case, the correlation coefficient between Bookface time and working time is -0.5.
The formula for the slope (b) can be calculated as b = r * (SDy / SDx), where r is the correlation coefficient and SDy and SDx are the standard deviations of the response variable and predictor variable, respectively.
Given that the standard deviation in Bookface time is 4.86 (SDx) and the standard deviation of time spent working is 3.50 (SDy), we can substitute these values into the formula:
b = -0.5 * (3.50 / 4.86)
Simplifying the expression:
b = -0.5 * 0.719
b ≈ - 0.3595
So, the value of the slope (b) is approximately -0.3595.
Now, to determine the value of the intercept (a) in the equation ŷi = a + bxi, we need additional information such as the mean values of Bookface time and time spent working.
Without knowing the mean values, we cannot calculate the intercept value (a) accurately. Thus, based on the provided information, we cannot determine the complete equation ŷi = a + bxi.