Use the method of least squares to fit a straight line to the five data points. (x): -2 -1 0 1 2 (y): 4 3 3 1 -1 a) Construct Y and X matrices for the data. b) Find X'X and X'Y. c) Find the least squares estimates B = (X'X)-'X'Y. Hint: The inverse of a diagonal matrix 1 d11 0 0 0 d22 0 0 0 d11 ... ... 1 d22 ... .. D = is D-1 ... ... 0 0 dnn 0 0 1 ... ... dnn d) Provide the fitted regression equation. Obtain a point estimate for the mean of Y when X = 1. Calculate the residual.
Inverse Normal Distribution
The method used for finding the corresponding z-critical value in a normal distribution using the known probability is said to be an inverse normal distribution. The inverse normal distribution is a continuous probability distribution with a family of two parameters.
Mean, Median, Mode
It is a descriptive summary of a data set. It can be defined by using some of the measures. The central tendencies do not provide information regarding individual data from the dataset. However, they give a summary of the data set. The central tendency or measure of central tendency is a central or typical value for a probability distribution.
Z-Scores
A z-score is a unit of measurement used in statistics to describe the position of a raw score in terms of its distance from the mean, measured with reference to standard deviation from the mean. Z-scores are useful in statistics because they allow comparison between two scores that belong to different normal distributions.
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