76 THE SIMPLE LINEAR REGRESSION MODEL (x – x)² y - y (x – F)(y – F) y 6. 1 2 2 3 1 4 Ex, = Ey, = E(x, – x) = E(x, – x)² E(y, – 5) = E(x, – x)(y; – y) = (a) Complete the entries in the table. Put the sums in the last row. What are the sample means F and ỹ? (b) Calculate b, and b, using (2.7) and (2.8) and state their interpretation. (c) Compute E1x, £z1xyi. Using these numerical values, show that E(xi – x)° = Ex} – NF and E(x – x)(yi – 5) = Exy; – Nãy (d) Use the least squares estimates from part (b) to compute the fitted values of y, and complete the remainder of the table below. Put the sums in the last row. Yi 6. 2 3 3 1 4 Ex E = %3! %3D (e) On graph paper, plot the data points and sketch the fitted regression line ŷi = bị + b,xj. (f) On the sketch in part (e), locate the point of the means (X, §). Does your fitted line pass through that point? If not, go back to the drawing board, literally. (g) Show that for these numerical values y = b| + bx. (h) Show that for these numerical values y = y, where y = £ÿ¡/N.
Percentage
A percentage is a number indicated as a fraction of 100. It is a dimensionless number often expressed using the symbol %.
Algebraic Expressions
In mathematics, an algebraic expression consists of constant(s), variable(s), and mathematical operators. It is made up of terms.
Numbers
Numbers are some measures used for counting. They can be compared one with another to know its position in the number line and determine which one is greater or lesser than the other.
Subtraction
Before we begin to understand the subtraction of algebraic expressions, we need to list out a few things that form the basis of algebra.
Addition
Before we begin to understand the addition of algebraic expressions, we need to list out a few things that form the basis of algebra.
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