333hmwk2-12 - Statistics 333 Nordheim Homework Assignment...

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Statistics 333 Feb 1, 2012 Nordheim Homework Assignment #2 -- Due Feb 8 1. The purpose of this exercise is to explore the meaning of degrees of freedom in regression. Suppose that you have 5 values of X and Y and you wish to fit a regression of Y on X. The estimated slope and intercept are and ˆ b 0 = 14.0 respectively. Below are the data --- with 2 of the Y values missing. Your job is to calculate the sum of squares for error. [Hint: Look at the definitional equations for slope and intercept and use simple algebra to calculate the missing “Y” values. Also, notice the simplification that results by considering the value for x .] X: -1 5 -6 2 0 Y; 12 18 1 ? ? If there were 20 measurements instead of 5, how many Y values would need to be specified so that you could calculate the sum of squares for error? Explain how this relates to degrees of freedom. 2. An experimenter was interested in the relationship between temperature and heart rate in the common grass frog. The temperature was manipulated in 2-degree increments ranging from 2 to 16 C with heart rates recorded at each temperature in beats per minute. (A different randomly selected frog was used at each temperature.) temp 2 4 6 8 10 12 14 16 heart rate 4 11 9 13 21 24 29 27 Find ( by hand calculation ) the least squares estimate of slope and intercept viewing heart rate as the dependent variable (i.e. heart rate as a function of temperature). Include a plot of heart rate versus temperature. Are your calculated estimates consistent with your plot? Explain. 3.
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This note was uploaded on 02/10/2012 for the course STAT 333 taught by Professor Rick during the Spring '11 term at Wisconsin Milwaukee.

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333hmwk2-12 - Statistics 333 Nordheim Homework Assignment...

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