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d. What percent of females have a graduation degree?
Ans. 37/282 = 13.12%
4. Find the Pearson’s coefficient of correlation between farmer education and yearly farm yield from the following
data:
No. of years of farmer education 0 2 4 6 8 10
Yield per year 4 4 6 10 9 7
Ans. x y xy x 2 y 2
0 4 0 0 16
2 4 8 4 16
4 6 24 16 36
6 10 60 36 100
8 9 72 64 81
10 7 70 100 49
2
Σx=30 Σy=40 Σxy=234 Σx =220 Σy =298
2
N = No. of samples = 6
N Σxy − (Σx) (Σy)
r =
2
N Σx − (Σx) ][NΣy – (Σy) ]
2
2
2
6(234) – (30) (40) 204
= = 0.72
2
2
6(220) – (30) (6(298) – (40) ) 280.99
5. Define the following terms and give examples from real life:
a. Positive Correlation
b. Causation
c. Negative Correlation
d. Outlier
Ans. a. Positive Correlation: Positive correlation is the relationship between two variables, in which both variables
have a linear relationship. As one variable increases/decreases, the second variable too increases/decreases.
For example, when fuel prices increase, prices of airline tickets also increase.
b. Causation: Causation shows that an event is the direct result of the occurrence of another event, i.e. a causal
relationship exists between the two events. This is also called cause and effect. For example, a speeding car
leads to an accident. The accident is due to causation.
c. Negative Correlation: Negative correlation is the relationship between two variables, where one variable
increases as the second variable decreases, and vice versa. For example, more exercising leads to a decrease
in body weight.
d. Outlier: In statistics, outliers are data points that are significantly different from other observations. Outliers
may be due to measurement irregularity or may indicate experimental error; the latter are sometimes
excluded from the data set. Outliers can cause serious problems in statistical analysis.
C. Competency-based/Application-based questions:
The following question consist of two statements: Assertion (A) and Reason (R).
Assertion (A): The dependent variable is the variable under study, and it is the variable that the regression model tries
to predict.
Regression 291

