本次CS代写的主要涉及如下领域: 北美程序代写,加拿大程序代写

Stat 151: Introduction to Applied Statistics

 

 

Assignment 2                                                                                                                               Total Marks: 65

Please read the following instructions carefully:

 

1. Assignment 2 is composed of THREE parts: Part 1: Lecture Problems and Part 2:  Combined Lab  and Lecture Problems, Part 3: Practice Problems (not for grading).
2. For Part 1, please complete all of the assigned exercises by hand. In Part 2, use procedures you were taught in the lectures and you may either type the answers or write them by hand.
3. Please organize and clearly label your solutions to each problem and staple ALL of your solutions together and hand them in altogether as instructed.

 

 

Part 1: Lecture Problems

 

Σ                 Σ                   Σ                    Σ                        Σ

From the Course Textbook: 14.40, 14.62, 14.102, 14.122, 14.126, 14.128, 14.132, 14.150

 

Summaries for 14.62, 14.102:      xi = 178,      yi = 1593,      x2 = 3522,       y2 = 302027,       xiyi = 32476

Summaries for 14.150:

xi = 668,

yi = 742,

xi = 44700,

Σ                  Σ                 Σ 2

i                2                 i        Σ

 

 

 

 

yi = 56622,

xiyi = 49596

Σ

14.40 For which of the following sets of data points can you  reasonably determine a regression line?  Explain  your answer. (2 marks)

1. 62. Crown-Rump Length. In the article “The Human Vomeronasal Organ. Part II: Prenatal Develop- ment” (Journal of Anatomy , Vol. 197, Issue 3, pp. 421–436), T. Smith and K. Bhatnagar examined the controversial issue of the human vomeronasal organ, regarding its structure, function, and identity. The following table shows the age of fetuses (x), in weeks, and length of crown-rump (y), in millimeters.

(20 Marks: 6 Marks for a., 4 Marks for b., and 2 Marks for each of c. – g.)

 

x	10	10	13	13	18	19	19	23	25	28
y	66	66	108	106	161	166	177	228	235	280

 

 

 

The summaries of the data are: Σ xi = 178, Σ yi = 1593, Σ x2 = 3522, Σ y2 = 302027, Σ xiyi = 32476.

i                                  i

 

1. 1. 1. find the regression equation for the data points.
      2. graph the regression equation and the data points.
      3. describe the apparent relationship between the two variables under consideration.
      4. interpret the slope of the regression line.
      5. identify the predictor and response variables.
      6. identify outliers and potential influential observations.
      7. predict the crown-rump length of a 19-week-old fetus.

 

x 10    10     13      13      18      19      19      23      25      28 y 66    66    108    106    161    166    177    228    235    280

14.102 Crown-Rump Length.  Following  are the data on age and crown-rump length for fetuses from  14.62.  (12 Marks: 5 Marks for a., 2 Marks for b., 3 Marks for c., and 2 Marks for d.)

 

 

 

i

i

The summaries of the data are: Σ xi = 178, Σ yi = 1593, Σ x2 = 3522, Σ y2 = 302027, Σ xiyi = 32476.

 

1.  

Σ

compute SST, SSR, and SSE, using Formula 14.2 on page 641. The formulae for SST, SSR, and

SSE are as follows:

 

 

SST =

 

Σ y2 −

 

(     yi)2 n

SSR =

 

[     x y    (     x     y ) /n]2

 

i

i

Σ             Σ     Σ−i   i                              i            i

Σ x2 − (Σ xi)2 /n

SSE = SST − SSR.

2. compute the coefficient of determination, r2.
3. determine the percentage of variation in the observed values of the response variable explained by the regression, and interpret your answer.
4. state how useful the regression equation appears to be for making predictions.

 

In 14.122 - 14.126, fill in the blanks.

 

14.122	A value of r close to              indicates that there is either no linear relationship between the variables or
14.126	a weak one. (1 Mark) If y tends to decrease linearly as x increases, the variables are                linearly correlated. (1 Mark)
14.128	Determine whether r is positive, negative, or zero. (1 Mark)

 

 

 

 

14.132 The linear correlation coefficient of a set of data points is 0.846. (3 Marks: 2 for a., 1 Mark for b.)

1. Is the slope of the regression line positive or negative? Explain your answer.
2. Determine the coefficient of determination.

14.150 Height and Score. A random sample of 10 students was taken from an introductory statistics class.  The following data were obtained, where x denotes height, in inches, and y denotes score on the final  exam. (8 Marks: 2 Marks for a., 6 Mark for b.)

 

x	71	68	71	65	66	68	68	64	62	65
y	87	96	66	71	71	55	83	67	86	60

 

i

i

The summaries of the data are: Σ xi = 668, Σ yi = 742, Σ x2 = 44700, Σ y2 = 56622, Σ xiyi = 49596.

 

1. What sort of value of r would you expect to find for these data? Explain your answer.
2. Compute r.

 

 

Part 2: Lab Problems

Complete the following: LAB 14.1, 14.2

 

 

LAB 14.1 Recently, statistics students at MacEwan completed a survey. Raw data can be found in the file STATISTICSSTUDENTSSURVEY. It contains the columns MOAGESTUDBIRTH (a variable that measures the age of a student’s mother when the student was  born) and  YRSFIRSTPHONE (a variable that measures the   age at which students got their first mobile  phone).  A  scatterplot  of  these  two  variables  can  be  found  below. Make sure you can create it. (14 marks: 1 mark for a, 1 mark for b, 2 marks for c, 2  marks for d, 1 mark for e, 1 mark for f, 3 marks for g, 3 marks for h)

 

 

1. What is the range of data for the ages at which students obtained their first mobile phone?
2. What is the range of data for the ages of mothers when their student children were born?
3. Is there a discernible pattern to this data? Why do you think you see what you see?
4. Assuming that there is no typo in the data, notice that one student appears to be an outlier in our data. That student was born when their mother was 32 years old and did not obtain their first mobile phone until they were 26 years old. Suggest a possible reason for this.
5. Find the equation for the line of best fit for this data.
6. Find the correlation for this data.
7. Write down the correct answer from those within the brackets.
   1. The correlation between these two variables is (mild, moderate, strong) and (positive, negative).
   2. The slope of the line of best fit for this data is (positive, negative).
   3. The correlation coefficient of two variables and the slope of the line of best fit through the two variables will always have (different, the same) sign.
8. Predict the age in years when a student obtained their first phone for a mother who was 50 years old when the student was born. Give two reasons why you would not be comfortable with the prediction.