A study of reading ability in schoolchildren chose 60 fifth-grade children at random from a school. The researchers had children's scores on an IQ test and on a test of reading ability. An eccentric professor has his own idea of the relationship between IQ and reading scores. He believes that an IQ of 100 should produce a reading score 43, and that reading score should increase by 1.1 points for every additional point of IQ. What is the equation of the professor's line?
Reading score = _______+________ IQ
Where a is intercept and b is the slope (1.1)
How do I find the intercept
we can solve by using formula
To find the intercept of the professor's line, we need to substitute the given values into the equation of a line, which is in the form of y = mx + b, where y is the dependent variable (reading score), x is the independent variable (IQ), m is the slope, and b is the intercept.
The given information states that an IQ of 100 should produce a reading score of 43. Plugging these values into the equation, we have:
43 = 1.1(100) + b
Now we need to solve for b, which represents the intercept. Simplifying the equation:
43 = 110 + b
Rearranging the equation to isolate b:
b = 43 - 110
b = -67
Therefore, the equation of the professor's line is:
Reading score = 1.1 IQ - 67