The number of words was noted in each of 100 sentences selected at random from two political thrillers written by different authors; 50 sentences were selected from each book. A summary of the data is given in the table (see attachment).

The two-sample z-test is to be used to investigate whether there is a difference, at the 5% significance level, between the mean length of sentences in the book by author A and the mean length of sentences in the book by author B.

21. choose the option that gives, to two decimal places, the estimated standard error of the difference between the two population means.
A 0.45 B 0.79 C 1.10 D 3.18 E 6.01 F 10.10

22. Choose the two options that give the value to two decimal places of the magnitude of the test static z, and the construction obtained from the test.
A 0.25 B 0.56 C 0.64 D 0.79 E 3.01 F 3.63
G There seems to be a significant difference, at the 5% significance level, between the mean sentence length in the book by author A and that in the book by author B.
H There seems to be no significant difference, at the 5% significance level, between the mean sentence length in the book by author A and that in the book by author B.

In the article 'Some physical properties of lentil seeds' by K. Carman (Journal of Agricultural Engineering Research, vol. 63, no. 2, pp. 87-92, 1996), the relationship between the moisture content and projected area of lentil seeds is modelled by a least square fit line. (The projected area of a seed is the area of its shadow on a plane surface when the light rays are perpendicular to the surface.) The least square fit line has equation y = 52.16 + 0.964x, where x is the moisture content in %d.b. (dry basis) and y is the projected area in mm^2.

23. Choose the option that, according to this model, is closest to the predicted projected area of a lentil seed with moisture content 15% d.b.
A 37.7 B 38.55 C 52.16 D 53.12 E 66.62 F 783.36

24. Suppose that the moisture content of lentil seed A is 10% d.b. greater than the moisture content of lentil seed B. Choose the option that, according to this model, is closest to the predicted amount (in mm^2) by which the projected area of the lentil seed A exceeds that of lentil seed B.

This posting contains the attachment with the solutions to the given problem. It shows the step-by-step procedures and explanations on how the answers are obtained.

The following readings were taken in a laboratory experiment:
x | 0 | 5 | 10 | 15 |
-----------------------------------------
y | 3000 | 3501 | 4022 | 4525 |
Determine the equation of the form y = mx + b that fits the data in a leastsquares sense.
(1) y = 101.92x + 2997.6
(2) y = x + 3000

The presence of autocorrelation leads to all of the following undesirable consequences in the regression results except:
a the least-squaresestimates of the regression coefficients will be biased
b the t-statistics may yield incorrect conclusions concerning the significance of the individual independent variables

"The linear regression line is sometimes called the leastsquaresline. Why?"
What is the idea of "leastsquares"?
What is the connection between "leastsquares" andlinear regression?
Could "leastsquares" and regression be generalized to more complicated cases than lines?

1. The leastsquares regression line given above is said to be a line which "best fits" the sample data. The term "best fits" is used because the line has an equation that minimizes the ______, which for these data is______.
2. For the data point (225.3, 308.1), the value of the residual is_____. (Round your answer to at le

Refer to the list below to answer the questions.
X 0 -1 1 1 2
y 2 -2 5 4 6
1. Find an equation of the leastsquares regression line. Please show your work.
2. Is there a linear correlation between "x" and "y" at the 0.01 significance level? Please just

1. Describe what a line is that satisfies the least-squares property-what is it and what is the function? (Please share your own way of understanding it).
2. This week we looked at regression analysis. What is the difference between a simple regression analysis and multiple regression? Please give examples.

In fitting a leastsquaresline to n=15 data points, the following quantities were computed: SSxx=55, SSyy=198, SSxy=-88, x-bar=1.3, and y-bar=35.
a.) Find the leastsquaresline.
b.) Describe the graph of the leastsquaresline.
c.) Calculate SSE
d.) Calculate s^2.

The variation attributable to factors other than the relationship between the independent variables and the explained variable in a regression analysis is represented by:
a. regression sum of squares.
b. error sum of squares.
c. total sum of squares.
d. regression mean squares.