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HP 30S Statistics – Linear Regression

Linear Regression Practice Solving Linear Regression Problems

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HP 30S Statistics – Linear Regression Linear regression A regression of y on x is a way of predicting values of y when values of x are given. If the regression is based on a straight line graph, it is called a linear regression, and the straight line is called the regression line. The regression line (sometimes referred to as the line of best fit) of y on x is then the line that gives the best prediction of values of y from those of x, and is:

y = a + bx where a=

∑ y i − b∑ x i n and b =

∑ xiyi − ∑ xi2 −

∑ xi ∑ yi n (∑ x i ) 2 n

n being the number of data pairs. (Note that …exibir mais conteúdo…

This menu works much like the CONST menu. Answer: Expressed to two decimal digits, a = 1.22 and b = 0.85, therefore the regression line is: y = 1.22 + 0.85x . The correlation coefficient, is 0.91, which means that the correlation is positive and that it is quite a good fit since r is close to 1. However, exactly how far away from this value the correlation can be and the equation still be considered a good predictor is certainly a matter of debate.

Example 2: If the engineer adds 4 grams of the chemical, what will be the concentration in the final product? Solution: Predicted values can be easily calculated using the regression line, but the quickest way is to use the STATVAR menu again. Press b, select y ' and press y. The entry line now reads y ' ( ) with the blinking cursor placed on the right parenthesis. y ' returns a predicted y value given an x value, that is, returns 1.22 + 0.85 x (remember that these numbers are shown to two decimal digits in this document, but not on your calculator). Enter the given x value: 4and press yto calculate the predicted concentration.

Answer:

y ' ( 4) = 4.63. In many textbooks y ' is written as y . It is important to understand that the actual ˆ concentration may well be different.: the regression line is just a mathematical model of the reality.

Example 3: In order to obtain a concentration of 10.5, how much chemical should she add? Solution: Once again press b but select x ' this time, and