Answer:
(a) y = 34.27 + 7.79x
(b) r = 0.98 (nearest hundredth)
(c) strong, positive correlation - as the students spends more time studying, their test scores increase.
Step-by-step explanation:
Correlation measures how closely two variables are linked.
If two variables are correlated, you can draw a line of best fit on the scatter plot.
- Explanatory (independent) variable is drawn on the x-axis
- Response (dependent) variable is drawn on the y-axis.
Linear regression is a method for finding the equation of a line of best fit on a scatter plot.
The regression line of y on x is: y = a + bx
where a = y-intercept and b = gradient
If b is positive, the variables are positively correlated.
If b is negative, the variables are negatively correlated.
Part (a)
Inputting the data from the table into a calculator and using the statistical function:
a = 34.27272727
b = 7.792207792
Therefore, the linear equation is:
y = 34.27 + 7.79x
Part (b)
The correlation coefficient is the Product Moment Correlation Coefficient (r) and measures the strength of the linear correlation between two variables.
Again, inputting the data from the table into a calculator and using the statistical function:
r = 0.9815741571
⇒ r = 0.98 (nearest hundredth)
Part (c)
The r value is always between +1 and -1. The closer it is to +1 or -1, the stronger the correlation between the two variables.
- Values close to +1 mean a strong, positive correlation.
- Values close to -1 mean a strong, negative correlation.
- Values close to zero mean a weak correlation.
Therefore, as r is very close to +1, the correlation coefficient suggests a strong, positive correlation. In the context of the problem, this suggests that as the students spends more time studying, their test scores increase.
