Maths-
General
Easy
Question
Consider the variables x and y and the corresponding bivariate data .
a) Draw a scatter plot for the data.
b) Is there positive, negative or no correlation between x and y?
c) Fit a line of best fit by eye to the data on the scatter plot.
d) Use your line of best fit to estimate:
i) y when x=3.5
ii) y when x=0
iii) x when y=1.5
iv) x when y=5.5
Hint:
A trend line is used to describe a pattern or a behavior for a scatter plot. If the variables increase or decrease together, then there exists a positive correlation among them. Or else, they have a negative correlation.
We are asked to drawn the scatter plot, find the correlation, best fit line for the model and to estimate the value of x when y = 3.5, y = 0, y = 5.5, y = 1.5.
The correct answer is:
Step 1 of 4:
The coordinate points for the given table are:
(1,1),(2,2),(3,2),(4,3),(5,4),(6,4),(7,5).
The scatter plot based on the points is:
Step 2 of 4:
Here, the variables x and y increases and decrease together. Even though, the change is not linear,
they increase and decrease steadily.
Hence, the scatter plot has a positive correlation.
Step 3 of 4:
The trend line based on the scatter plot is:
Step 4 of 4:
The values of x when y = 3.5, y = 0, y = 1.5 and y = 5.5 are:
X = 5, x = 0, x = 2, x = 7.5
That is, the points are: (0, 0), (2,1.5), (5,3.5), (7.5,5.5).
We might not get the accurate values by analyzing the trend lines. Since, it approximates the pattern of the set of values.
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