Question

In: Statistics and Probability

Children's height as a function of their age has been researched so extensively that we can...

Children's height as a function of their age has been researched so extensively that we can consider known results to describe the relationship for all children in the United States. For instance, between the ages of 13 and 15, population mean height for teenage males (in inches) satisfies

μy = 22 + 3x,  where x is age in years. Spread about the line is 3.1 inches.

1.  Notice that the slope of the regression line for the population is β1 = 3. If we were to take repeated random samples of 25 males between the ages of 13 and 15 and regress their heights on their ages, then the slopes b1 would vary from sample to sample. At what slope value would their distribution be centered? (Answer as a whole number.)

2. On average, how much shorter do you predict a 13-year-old to be compared to a 15-year-old? (Answer as a whole number.)

3. The linear regression model does a good job of summarizing the relationship between height and age for males in a particular age range, such as between 13 and 15 years old. Which two conditions would not be met if we attempted to perform inference about the height/age relationship based on a random sample of 250 males all the way from newborn to 25 years old?

a. Scatterplot should appear linear.

b. Sample size should be large enough to offset non-normality in responses.

c. Spread of responses should appear fairly constant over the range of explanatory values.

d. Explanatory/response values should constitute a random sample of independent pairs.

Solutions

Expert Solution

1.  Notice that the slope of the regression line for the population is β1 = 3. If we were to take repeated random samples of 25 males between the ages of 13 and 15 and regress their heights on their ages, then the slopes b1 would vary from sample to sample. At what slope value would their distribution be centred? (Answer as a whole number.)

The slope will be centred at 3 as its the average value of all the values.

2. On average, how much shorter do you predict a 13-year-old to be compared to a 15-year-old? (Answer as a whole number.)

So on average, the difference will be 67-31=6 inches

3. The linear regression model does a good job of summarizing the relationship between height and age for males in a particular age range, such as between 13 and 15 years old. Which two conditions would not be met if we attempted to perform inference about the height/age relationship based on a random sample of 250 males all the way from newborn to 25 years old?

a. Scatterplot should appear linear.

d. Explanatory/response values should constitute a random sample of independent pairs.


Related Solutions

Housing prices in Athens have been researched extensively by faculty at UGA. The current thinking is...
Housing prices in Athens have been researched extensively by faculty at UGA. The current thinking is that housing prices follow an approximately normal model with mean $162,000 and standard deviation $7,034. (a) What proportion of housing prices in Athens are less than $153,000? (3 decimal places) (b) A realtor takes a random sample of 128 houses in Athens. Determine the probability the average selling price is greater than $163,000? (3 decimal places) (c) A realtor in Asheville, NC wants to...
Housing prices in Athens have been researched extensively by faculty at UGA. The current thinking is...
Housing prices in Athens have been researched extensively by faculty at UGA. The current thinking is that housing prices follow an approximately normal model with mean $186,000 and standard deviation $7,959. (a) What proportion of housing prices in Athens are less than $176,000? (3 decimal places) (b) A realtor takes a random sample of 123 houses in Athens. Determine the probability the average selling price is greater than $187,000? (3 decimal places) (c) A realtor in Asheville, NC wants to...
We are studying the relationship of age in years and height in inches for children of...
We are studying the relationship of age in years and height in inches for children of ages from 2 - 10. We have a sample of five children. It is a linear relationship, so please find: (a) r (b) r(sq); (c) the equation of the regression line (d) the expected height in inches for a 7 year-old child. Age(X) Height(Y) 2 37 3 40 3 42 6 47 9 54
It is important to note that we are assuming that so far there has been NO...
It is important to note that we are assuming that so far there has been NO governmental action regarding the virus. So, there has been no quarantining, there have been no “Stay-at-Home” orders, there have been no orders closing businesses, and, generally, there have been no decisions by a governmental entity regarding the virus.Draw a graph to explain your answer. First, explain (in words) what an “efficient” outcome is in the present context. Then, present an economic argument, using a...
Discuss the topic of maximizing shareholder wealth. This topic has been researched and studied for many...
Discuss the topic of maximizing shareholder wealth. This topic has been researched and studied for many years, with mixed results. For example; Irving Fisher, a prominent American Economist, argued that maximizing shareholders wealth should be management’s primary goal (Cardao-Pito, 2016). Conversely, Sollars and Tuluca (2016) suggested that shareholders should only be rewarded with returns that are “commensurate with the risk they take”. (p. 203). Briefly share your thoughts about shareholder wealth maximization. Then, explain the advantages and disadvantages of wealth...
Next, discuss the topic of maximizing shareholder wealth. This topic has been researched and studied for...
Next, discuss the topic of maximizing shareholder wealth. This topic has been researched and studied for many years, with mixed results. For example; Irving Fisher, a prominent American Economist, argued that maximizing shareholders wealth should be management’s primary goal (Cardao-Pito, 2016). Conversely, Sollars and Tuluca (2016) suggested that shareholders should only be rewarded with returns that are “commensurate with the risk they take”. (p. 203). After reading the required textbook chapters for this module, briefly share your thoughts about shareholder...
The Eight Queens Problem is a fairly old problem that has been well discussed and researched....
The Eight Queens Problem is a fairly old problem that has been well discussed and researched. The first published reference to this problem was in a German Chess magazine in 1848 by Max Bezzel. In 1850, Franz Nauck published all 92 solutions of the problem for an 8x8 board. S. Gunther in 1874 suggested a method for finding solutions by using determinants and J.W.L. Glaisher extended this method. E. Dijkstra published a detailed description of the solution of the problem...
It has been extensively demonstrated that adequate night sleep is crucial for cognitive performance.  To investigate whether...
It has been extensively demonstrated that adequate night sleep is crucial for cognitive performance.  To investigate whether first year USC students are getting adequate sleep the night before a final exam, 81 randomly selected first year USC students were asked to record their number of hours of sleep the night before their final exams. The mean number of hours of sleep among the 81 students was 6.2 with an SD of 1.5 hours.                                                                                       (18 points) Identify the population, sample, and parameter of...
Hi, so for my homework assignment, we are meant to change this function so that instead...
Hi, so for my homework assignment, we are meant to change this function so that instead of making a list from the array going up in an ascending order, making it be listed in descending order, meaning going from largest number to smallest number, the code I have now works for the ascending order, but how would I change this for it to go descending? Any help would be amazing, and please with a tutorial, thanks so much. def heapify(arr,...
9. The territorial behavior in Yarrow’s spiny lizard (Sceloporus jarrovi) has been studied extensively. a) Provide...
9. The territorial behavior in Yarrow’s spiny lizard (Sceloporus jarrovi) has been studied extensively. a) Provide evidence to briefly explain why the push-ups and head-bobbing displays behavior of Yarrow’s spiny lizard are probably honest signals of a lizard’s strength. (4 points)    b) Provide TWO hypotheses to briefly explain why you might expect a resident lizard to successfully repel intruders (i.e. don’t just name them). (6 points)    c) Under what conditions (characteristics of the two males) would you expect...
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT