The slope of the least squares regression line is 1.0 and the y-intercept is 6.3
How to determine the slope?
To do this, we enter the data values in a graphing calculator, and we interpret the results:
Using a graphing calculator, we have the following calculation summary
- Sum of X = 83
- Sum of Y = 123
- Mean X = 13.8333
- Mean Y = 20.5
- Sum of squares (SSX) = 356.8333
- Sum of products (SP) = 365.5
- R = 0.8728
The slope (b) is calculated using:
b = SP/SSX
This gives
b = 365.5/356.83
b = 1.0
Hence, the slope is 1.0
How to determine the y-intercept?
The y-intercept (a) is calculated using:
a = MY - bMX
a = 20.5 - (1.02*13.83)
a = 6.3
Hence, the y-intercept is 6.3
How to determine the correlation coefficient?
In (a), we have:
R = 0.8728
Approximate
R = 0.9
This means that the correlation coefficient is 0.9
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