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Example 4: Consider regression equation for 55 students with x = right forearm length (cm) and y = height. The forearm
lengths were in the range from 22 cm to 31 cm. The regression equation is:
y = 30.3 + 1.49x
Let us see some practice questions.
1. One student’s right forearm length was 27 cm, and his height was 76 inches. What is the estimated height for this
student, based on the regression equation? What is the residual?
Answer: Estimated Height => 30.3 + 1.49*27 = 70.53
Residual = y – ŷ => 76 – 70.53 = 5.47
Note that Residual = Observed value – Predicted value (e = y – ŷ). Each data point has one residual.
2. One student’s right forearm length was 22 cm, and her height was 62 inches. What is the estimated height for this
student, based on the regression equation? What is the residual?
Answer: Estimated Height => 30.3 + 1.49*22 = 63.08
Residual => 62 – 63.08 = –1.08
Reboot
1. State the two types of Regression.
2. How many variables are used in linear regression?
3. State the equation of the line of best fit?
4. Why is it called the line of best fit?
5. State two applications of regression.
Correlation
The word correlation is used in daily life to denote some forms of association. We might say that we have noticed a
correlation between smog and asthma attacks. However, in statistical terms, we use correlation to express an association
between two quantitative variables. It measures the strength or degree of relationship between two variables. The
relationship may be causal. We also presume that the association is linear, i.e., one variable increases or decreases a set
amount for a unit increase or decrease in the other.
Perfect High Low Low High Perfect
Positive Positive Positive No Negative Negative Negative
Correlation Correlation Correlation Correlation Correlation Correlation Correlation
282 Touchpad Artificial Intelligence (Ver. 2.0)-XI

