Question

QUESTION 21 Table4 No. of Commercials (x) Sales Volume (y) Using Table 4, what is the slope of the regression line (61)? abı = 3 b.61 - -2 Ocbi-3 d. by - 2 QUESTION 22 A professor finds out that 30% of students fail because they don't study (S), 20% of students fail because they work (W), and 12% of students fail because they work (W) and don't study (S). What is the probability that a student who fails does so because of lack of study (S) or because of work (W) or both? a. 0.50 6.0.62 C. 0.38 Od 0.42

Please answer questions 21 & 22

Answer 1

Solution :

21) Slope of a simple linear regression equation is given as follows :

$\large b_{1}=\frac{\sum_{i=1}^{n}(x_{i}-\bar{x})(y_{i}-\bar{y})}{\sum_{i=1}^{n}(x_{i}-\bar{x})^{2} }$

Where,

$\large \bar{x} = \frac{1}{n}\sum_{i=1}^{n}x_{i}, \bar{y}=\frac{1}{n}\sum_{i=1}^{n}y_{i}$

n = 5

$\large \bar{x} = \frac{1}{5}(3+12+6+20+14)$

$\large \bar{x} = \frac{55}{5}=11$

$\large \bar{y} = \frac{1}{5}(55+40+54+10+15)$

$\large \bar{y} = \frac{175}{5}=35$

$\large \sum_{i=1}^{n}(x_{i}-\bar{x})(y-\bar{y}) =\left [ (3-11)(55-35)+.................+(14-11)(15-35) \right ]$

$\large \sum_{i=1}^{n}(x_{i}-\bar{x})(y-\bar{y}) = -540$

$\large \sum_{i=1}^{n}(x_{i}-\bar{x})^{2} = \left [ (3-11)^{2}+.................+(14-11)^{2} \right ]$

$\large \sum_{i=1}^{n}(x_{i}-\bar{x})^{2} = 180$

$\large \therefore b_{1}=\frac{-540}{180}=-3$

Option (c) is correct.