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The regression line should be drawn on the scatter diagram in such a way that when the squared values of the vertical distance from each plotted point to the line are added, the total amount will be the smallest possible amount. This criterion is called the Method of Least Squares.
Minimizing the sum of the squared differences of each value of Y from the regression line by the method of calculus, we arrive at two equations, called the normal equations:
Solving these equations simultaneously, and using equivalent expressions for and , we obtain the following formulae used to calculate the coefficients a and b in the regression line = = a + bX
E(Y|X = x) = a + bx
A consumer preference study involving three different bottle designs (A, B, and C) for the jumbo size of a new liquid detergent was carried out using a randomized block experimenta
In 120 tosses of a coin, 45 heads and 75 tails are observed. Is this a balanced coin? Use a=0.05. (Follow the basic steps of hypothesis testing)
Let X 1 and X 2 be two independent populations with population means μ 1 and μ 2 respectively. Two samples are taken, one from each population, of sizes n 1 and n 2 re
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Zinc is a trace element and it is important in wound healing, building up the immune system and DNA synthesis. The data in Table 1 represents the zinc intake (in milligrams) for a
The decision maker ranks lotteries according to the utility function (i) State the independence assumption. Does this decision maker satisfy it? (ii) Is this decision ma
Mode The mode is the value which occurs most frequently in a set of observations on the point of maximum frequency and around which other items of the set cluste
Two individuals, player 1 and player 2, are competing in an auction to obtain a valuable object. Each player bids in a sealed envelope, without knowing the bid of the other player
1 A penny is tossed 5 times. a. Find the chance that the 5th toss is a head b. Find the chance that the 5th toss is a head, given the first 4 are tails.
Question: (a) A normal distribution is thought to have a mean of 50. A random sample of 100 gave a mean of 52.6 and a standard deviation of 14.5. A significance test was carri
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