A pediatrician wants to determine the relation that may exist between a​ child's height and head circumference. She randomly selects 5 children and measures their height and head circumference. The data are summarized below. Complete parts​ (a) through​ (f) below.

(a) Treating height as the explanatory variable, X, use technology to determine the estimates of β0 and β1.

β0 ≈b0 = ____ ​(Round to two decimal places as​ needed.)

β1 ≈b1 = ____ (Round to two decimal places as​ needed.)

​(b) Use technology to compute the standard of the estimate , se.

se= ______ ( Rounding to four decimal places)

​(c)  A normal probability plot suggests that the residuals are normally distributed . Use technology to determine sb1 .

Sb1= _____ ( Rounding to four decimal places)

(d) ​A normal probability plot suggests that the residuals are normally distributed. Test whether a linear relation exists between height and head circumference at the α=0.01 level of significance.

The first step is to set up a hypothesis test. The parameter being tested is the​ slope, β1​, of the linear regression line. If there is no linear relation between the response and explanatory​ variables, the slope of the true regression line will be zero.

The​ P-value for this test is _____ (rounding to three decimal places.)

(e) Use technology to construct a​ 95% confidence interval about the slope of the true​ least-squares regression line.

Lower bound: ____

Upper bound : _____

(f) Suppose a child has a height of 27 inches. What would be a good guess for the​ child's head​circumference?

Substitute the given​ height, 27​ inches, for x in the regression line and​ simplify, rounding to two decimal places.

Y= ______

Wal-Mart is the second largest retailer in the world. The data file (WalMart_revenue.xlsx) is included in the Excel data zip file in week one, and it holds monthly data on Wal-Mart’s revenue, along with several possibly related economic variables. Develop a linear regression model to predict Wal-Mart revenue, using CPI as the only (a) independent variable. (b) Develop a linear regression model to predict Wal-Mart revenue, using Personal Consumption as the only independent variable. (c) Develop a linear regression model to predict Wal-Mart revenue, using Retail Sales Index as the only independent variable. (d) Which of these three models is the best? Use R-square value, Significance F values and other appropriate criteria to explain your answer. Identify and remove the four cases corresponding to December revenue. (e) Develop a linear regression model to predict Wal-Mart revenue, using CPI as the only independent variable. (f) Develop a linear regression model to predict Wal-Mart revenue, using Personal Consumption as the only independent variable. (g) Develop a linear regression model to predict Wal-Mart revenue, using Retail Sales Index as the only independent variable. (h) Which of these three models is the best? Use R-square values and Significance F values to explain your answer. (i) Comparing the results of parts (d) and (h), which of these two models is better? Use R-square values, Significance F values and other appropriate criteria to explain your answer. Please use one Excel file to complete this problem, and use one sheet for one sub-problem. Use a Microsoft Word document to answer questions. Finally, upload the files to the submission link for grading.

Three genes in fruit flies affect a particular trait, and one dominant allele of each gene is necessary to get a wild-type phenotype. What phenotypic ratios would you predict among the progeny if you crossed triply heterozygous flies?

Multiple Choice

• 27:64

• 9:23

• 37:64

• 1:3

• 27:37

• 3:5

• 1:7

Would the answer be 27:37 wild to mutant?

According to a report by Scarborough Research, the average monthly household cellular phone bill is $73. Suppose local monthly household bills are normally distributed with a standard deviation of $11.35.

(a) What is the probability that a randomly selected monthly cellphone bill is between $60 and $74?

(b) What is the probability that a randomly selected monthly cellphone bill is between $79 and $88?

(c) What is the probability that a randomly selected monthly cellphone bill is no more than $39?

2. Let’s use the data from the sea ice extent by year. a. Do a t-test to determine if the slope = 0, give null and alternative hypotheses, test statistic, pvalue, decision and interpretation. b. Construct a residual plot vs fitted values. c. Look at a histogram of the residuals. d. Are there any obvious outliers? Find that observation that is the most glaring and find out how many standard deviations it is from the mean. Can this be justified to be removed? e. Are the assumptions for regression met? (Linearity, Constant Standard Deviation and Normality of errors). If not, which one is violated.

data:

Year Extent

1980 9.18

1981 8.86

1982 9.42

1983 9.33

1984 8.56

1985 8.55

1986 9.48

1987 9.05

1988 9.13

1989 8.83

1990 8.48

1991 8.54

1992 9.32

1993 8.79

1994 8.92

1995 7.83

1996 9.16

1997 8.34

1998 8.45

1999 8.6

2000 8.38

2001 8.3

2002 8.16

2003 7.85

2004 7.93

2005 7.35

2006 7.54

2007 6.04

2008 7.35

2009 6.92

2010 6.98

2011 6.46

2012 5.89

2013 7.45

2014 7.23

2015 6.97

2016 6.08

2017 6.77

2018 6.13

2019 5.66

By using the definition and discussing what is relevant to the situation, interpret each of the following for both the coffee and tea data. Also, compare each for coffee and tea. Be sure to include the relevant information (state the value of or, in the case of the distribution, include the graphs) with each component.

1. Mean
2. Median
3. Modal Interval
4. Range
5. IQR
6. Standard Deviation
7. Distribution of histogram and box plot
8. Slope of each linear model
9. Y-intercept of Coffee vs. Tea
10. Correlation coefficient for each linear model
11. Relevant interpolations or extrapolations
12. Correlation type (from Activity 5) for coffee and tea

Historical average returns for Large Company Common Stocks, Long Term Government Bonds, and US Treasury Bills for the period 10-year period of 1999 through 2008 are shown in the following table. Use these data to solve the next several problems.

1. Calculate the average return for Large Company Common Stocks for the 10-year period.

2. Calculate the average return for Long Term Corporate Bonds for the 10-year period.

3. Calculate the average return for US T-bills for the 10-year period.

4. Calculate the holding period return for Large Company Common Stocks for the 10-year period.

5. Calculate the holding period return for Long Term Corporate Bonds for the 10-year period.

6. Calculate the holding period return for US T-bills for the 10-year period.

Consider the following Data:

By using the definition and discussing what is relevant to the situation, interpret each of the following for both the coffee and tea data. Also, compare each for coffee and tea. Be sure to include the relevant information (state the value of or, in the case of the distribution, include the graphs) with each component.

1. Mean
2. Median
3. Modal Interval
4. Range
5. IQR
6. Standard Deviation
7. Distribution of histogram and box plot
8. Slope of each linear model
9. Y-intercept of Coffee vs. Tea
10. Correlation coefficient for each linear model
11. Relevant interpolations or extrapolations
12. Correlation type for coffee and tea

Please answer the following questions based on the given graph

(1) Create a Time Series (Trend)Model  for  passengers on Domestic flights. (To zero decimal places) The predicted amount of passengers for 2010 on Domestic flights is ________.

(2) Create a Time Series (Trend)Model  for  passengers on Domestic flights. (To zero decimal places) On average, the number of passengers of domestic flights increase by ________each year, keeping all else equal.

(3)Create a GrowthModel  for  passengers on Domestic flights. (To zero decimal places) The predicted amount of passengers for 2010 on Domestic flights is ________.

(4)Create a Growth Model  for passengers on Domestic flights. (To two decimal places) On average, the number of passengers of domestic flights increase by ________percent each year, keeping all else equal.

(5) Based on R-squared which model is better for predicting passengers of domestic flights?
Time Series (Trend) Model
Growth Model