Question

4. At a recent carnival Mr. Clairvoyant claimed that he could guess the weight of females within one pound by studying the lines in their hands and fingers. He measured the females' fingers and guessed their weights. Below is the data for 5 of the females. Female Finger Length (cm) Weight (lb) 6.0 3.7 154 165 154 a) Determine the equation Mr. Clairvoyant would use to predict weight from finger length (6 marks) b) If Mr. Clairvoyant were to graph his regression line what would the y-intercept be? What would the slope be? (2 marks) c) What weight would he predict for a female whose fingers were 3.2 cm long? (2 marks)

Answer 1

a)

The following data are passed: Figure length(cm) Weight (lb) 125 136 154 165 154 172 The independent variable is Figurelength(cm), and the dependent variable is Weight(lb). In order to compute the regression coefficients, the following table needs to be used: Figure length(c Weight (lb) Figure length(c m)*Weig ht (lb) Figure length(c Weight (lb)2 m2 125 637.5 26.01 15625 6 136 816 36 18496 154 569.8 13.69 23716 726 27225 4.4 4.6 4.5 165 154 172 708.4 19.36 21.16 20.25 23716 774 29584 Sum = 28.3 906 4231.7 136.47 138362 Based on the above table, the following is calculated: 28.3 * = x = 28,3 – 4.71666666667 = 4.7166666666667 906 n Y; = = 151

SSxx = X = 136.47 – 28.3/6 = 2.9883333333333 85*8 = 3x3 ++ (2x) – 1647 – 237/6 – 29889sage 95y = $x -- (37) – 1862 – 90°) - 1556 S88v = {xx - + (2x) (3x) – 4231.7 –283 x 306/6 – – 41.509 SSYY =) 138362 - 9062/6 = 1556 n2 =1 Therefore, based on the above calculations, the regression coefficients (the slope m, and the y-intercept n) are obtained as follows: m = od SSXY SSxx -41.599999999999 2.9883333333333 = -13.9208 n=Y - Xm = 151 - 4.7166666666667 (-13.9208) = 216.6598 Therefore, we find that the regression equation is: Weight(lb) = 216.6598 - 13.9208 Figurelength(cm) Graphically Scatter Plot and Regression Line 115.9024 3.44 3.64 3.84 4.04 4.24 4.44 4.64 4.84 5.04 5.24 5.44 5.64 5.84 6.04 6.24 6.44
b) The general regression equation is given by

Y = a +bX

The coefficient b is known as the slope coefficient, and the coefficient a is known as the y-intercept.
here y-intercept : a = 216.6598
Slope : b = -13.9208

c) figure length is 3.2 cm
Let regression equation be
Weight(lb)=216.6598−13.9208Figurelength(cm)

Weight (lb) = 216.6598 - 13.9208 * 3.2
Weight (lb) = 216.6598 - 44.54656
Weight(lb) = 172.11324

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