代写Introduction to Quantitative Methods ASSIGNMENT 2代写留学生Matlab程序

ASSIGNMENT 2

10 points

Q1     (2.5 points)

An accurate assessment of soil productivity is critical to rational land-use planning. Unfortunately, as the author of the article “Productivity Ratings Based on Soil Series” (Prof. Geographer, 1980: 158–163) argues, an acceptable soil productivity index is not so easy to come by. One difficulty is that productivity is determined partly by which crop is planted, and the relationship between yield of two different crops planted in the same soil may not be very strong. To illustrate, the article presents the accompanying data on corn yield x and peanut yield y (mT/ha) for eight different types of soil.

x	2.4	3.4	4.6	3.7	2.2	3.3	4.0	2.1
y	1.33	2.12	1.80	1.65	2.00	1.76	2.11	1.63

Calculate the sample correlation coefficient Q2        (2.5 points)

In some locations, there is a strong association between concentrations of two different pollutants. The article “The Carbon Component of the Los Angeles Aerosol: Source Apportionment and Contributions to the Visibility Budget” (J. Air Pollution Contr. Fed.,  1984: 643–650) reports the accompanying data on ozone concentration x (ppm) and secondary carbon concentration y (mg/m3).

x	.066	.088	.120	.050	.162	.186	.057	.100
y	4.6	11.6	9.5	6.3	13.8	15.4	2.5	11.8

x

.112

.055

.154

.074

.111

.140

.071

.110

y

8.0

7.0

20.6

16.6

9.2

17.9

2.8

13.0

Calculate the point estimate of the population correlation coefficient r between ozone concentration and secondary carbon concentration Q3     (2.5 points)

Global warming is a major issue, and CO2 emissions are an important part of the discussion. What is the effect of increased CO2 levels on the environment? In particular, what is the effect of these higher levels on the growth of plants and trees? The article “Effects of Atmospheric CO2  Enrichment on Biomass Accumulation and Distribution in Eldarica Pine Trees” (J. Exp. Bot.,  1994: 345–349) describes the results of growing pine trees with increasing levels of CO2 in the  air. There were two trees at each of four levels of CO2 concentration, and the mass of each tree  was measured after 11 months of the experiment. The table below shows the observations with x  = atmospheric concentration of CO2 in microliters per liter (parts per million) and y = mass in  kilograms, along with x2, xy andy2. The mass measurements were read from a graph in the article.

Obs.	x	y
1	408	1.1
2	408	1.3
3	554	1.6
4	554	2.5
5	680	3.0
6	680	4.3
7	812	4.2
8	812	4.7

a). Estimate that the expected change in tree mass associated with a 1-part-permillion increase in CO2 concentration.

b). Write down the equation of the estimated regression line (least squares line)

Q4     (2.5 points)

The excel sheet (Homework Data) contains data for the linear regression equation

Y = β0  + β 1X1  + β2X2  +β3X3  + ԑ

Where

Y = Sales

X1  = Product Price

X2  =  Product Quality

X3  = Shop Space 3

a)  Using the Statistical Package for Social Sciences (SPSS) calculate the mean, standard deviation, minimum and maximum values of each variable in the equation.

b)  Estimate the correlation coefficients of the variables in the equation

c)   Estemate the ANOVA table and the regression coefficients.