Q.4:-Weight (V) is regressed on height(x) of 40 adults. The height range in the data is 50-100 and the regression line is Y = 100+0.1X with R²=0.12. Which of the conclusions below does not necessarily low
The data suggests a weak relationship between X and Y
An adult with an X-value of 60 has an estimated Y-value of 106
An adult with an X-value of 80 has an estimated Y-value of 108
An adult with an X-value of 90 has an estimated Y-value of 109
Answers
Weight (V) is regressed to the height(x) of 40 adults. The height range in the data is 50-100 and the regression line is Y = 100+0.1X with R²=0.12.
Hence the final answer is :
Y value of the world does not necessarily low
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Concept
Regression is a statistical tool used to relate a dependent variable to one or more independent variables.
Given
Weight (V) is regressed on height(x) of 40 adults.
regression line is Y = 100+0.1X with R²=0.12.
Find
we need to find which of the given conclusions below does not necessarily follow
Solution
We have
Y = 100+0.1X
Here, if X = 60,
Y = 100 + 0.1(60)
Y = 100 + 6
Y = 106
Thus, 2 follows.
if X = 80,
Y = 100 + 0.1(80)
Y = 100 + 8
Y = 108
Thus, 3 follows.
if X = 80,
Y = 100 + 0.1(90)
Y = 100 + 9
Y = 109
Thus, 4 follows.
Now, 1 is the only option left, it must be the answer. Moreover, a low R squared value does not necessarily suggests a 'weak relationship' between variables.
Hence, option 1 does not necessarily follow.
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