The heights (inches) and foot lengths (cm) of 33 college men are shown in the dataset. Student Height Foot Length 1 66.5 27.0 2 73.5 29.0 3 70.0 25.5 4 71.0 27.9 5 73.0 27.0 6 71.0 26.0 7 71.0 29.0 8 69.5 27.0 9 73.0 29.0 10 71.0 27.0 11 69.0 29.0 12 69.0 27.2 13 73.0 29.0 14 75.0 29.0 15 73.0 27.2 16 72.0 27.5 17 69.0 25.0 18 68.0 25.0 19 72.5 28.0 20 78.0 31.5 21 79.0 30.0 22 71.0 28.0 23 74.0 29.0 24 66.0 25.5 25 71.0 26.7 26 71.0 29.0 27 71.0 28.0 28 84.0 27.0 29 77.0 29.0 30 72.0 28.0 31 70.0 26.0 32 76.0 30.0 33 68.0 27.0 If the person who reportedly is 84 inches tall is excluded, the regression equation for the remaining 32 men is expressed with the following formula. ŷ = 0.253 + 0.384x (a) How much does average foot length increase (in cm) for each 1-inch increase in height? (Round your answer to three decimal places.) cm (b) Predict the difference in the foot lengths (in cm) of men whose heights differ by 10 inches. (Round your answer to two decimal places.) cm (c) Suppose Max is 62 inches tall and has a foot length of 24.80 centimeters. On the basis of the regression equation, what is the predicted foot length (in cm) for Max? (Round your answer to two decimal places.) cm What is the value of the prediction error (residual) for Max (in cm)? (Round your answer to two decimal places.

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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.