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N = No. of samples = 5
m = N Σ(xy) − Σx Σy
N Σ(x ) − (Σx) 2
2
5(64) – (10) (25)
=
5 (30) – (10) 2
320 – 250
=
150 – 100
70
=
50
Σy − m Σx
b =
N
25 – 1.4 (10)
= = 2.2
5
Putting the values in the equation y = mx + b, we get the regression equation
y = 1.4 x + 2.2
b. When x = 10,
y = 1.4 (10) + 2.2 = 16.2
2. Describe the four assumptions for Pearson's correlation coefficient.
Ans. There are some assumptions for Pearson's correlation coefficient which are as follows. If any of these four
requirements are not met, analysis of data using Pearson's correlation coefficient might not yield a valid result.
(a) The data type of the two variables should be continuous.
(b) There must be a linear relationship between the two variables. Create a scatterplot by plotting the two
variables against each other. The scatterplot can then be used to check for linearity.
(c) The data should not have any significant outliers. Outliers can have a great impact on the line of best fit and
the Pearson correlation coefficient, leading to very difficult inferences regarding the data. Hence, it is best to
have no outliers or keep them to a minimum.
(d) The variables should be normally distributed (approximately).
3. The table below shows the crosstab of gender and highest education degree achieved by 500 people in a survey:
No Secondary Secondary Higher Secondary Graduation Post Graduation Total
School Degree School Degree School Degree Degree Degree
Males 50 95 11 39 23 218
Females 52 166 15 37 12 282
Total 102 261 26 76 35 500
Calculate:
a. What percent of the sample were males?
Ans. 218/500 = 43.6%
b. What percent of the sample were males with no secondary school degree?
Ans. 50/500 = 10%
c. What percent of the people did not graduate from secondary school?
Ans. 102/500 = 20.4%
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