ZIMS store sells its products on installments in Karachi. The store decided to investigate the link between the life of the product and the cost. The data collected from store is shown in Table 1.1 Table 1.1 LIFE OF PRODUCT (Years) COST (Thousand Rupees) 3.0 25 3.5 28 4.0 32 4.5 34 5.0 34 3.0 30 5.5 40 4.5 40 4.0 42 3.5 42 6.0 50 7.5 50 8.0 53 8.5 55 a) Plot a scatter chart from the above data. b) Find the equation of the least square regression line in the form ? = ? + ?? Given the value of a and b up to 3 decimal places. c) What are the exact interpretations of the estimated regression factors? d) Using your answer of part (b). Find the cost predicted by the regression line for 6.5 year’s life of a product.
Continuous Probability Distributions
Probability distributions are of two types, which are continuous probability distributions and discrete probability distributions. A continuous probability distribution contains an infinite number of values. For example, if time is infinite: you could count from 0 to a trillion seconds, billion seconds, so on indefinitely. A discrete probability distribution consists of only a countable set of possible values.
Normal Distribution
Suppose we had to design a bathroom weighing scale, how would we decide what should be the range of the weighing machine? Would we take the highest recorded human weight in history and use that as the upper limit for our weighing scale? This may not be a great idea as the sensitivity of the scale would get reduced if the range is too large. At the same time, if we keep the upper limit too low, it may not be usable for a large percentage of the population!
ZIMS store sells its products on installments in Karachi. The store decided to investigate the link between the life of the product and the cost. The data collected from store is shown in Table 1.1
Table 1.1
LIFE OF PRODUCT (Years) COST (Thousand Rupees)
3.0 25
3.5 28
4.0 32
4.5 34
5.0 34
3.0 30
5.5 40
4.5 40
4.0 42
3.5 42
6.0 50
7.5 50
8.0 53
8.5 55
a) Plot a scatter chart from the above data.
b) Find the equation of the least square regression line in the form ? = ? + ??
Given the value of a and b up to 3 decimal places.
c) What are the exact interpretations of the estimated regression factors?
d) Using your answer of part (b). Find the cost predicted by the regression line for 6.5 year’s life of a product.
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