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.
<h3><u>Part (a)</u></h3>
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
<h3><u>Part (b)</u></h3>
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)
<h3><u>Part (c)</u></h3>
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.
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