Calculate the least-squares line

Reference no: EM132243589

Basic Statistics Assignment Questions -

Question 1 - The maximum discount value of the Entertainment card for the "Fine Dining" section, Edition ten, for various pages is given in Table.

Page Number	Maximum Value ($)
4	16
14	19
25	15
32	17
43	19
57	15
72	16
85	15
90	17

a. Decide which variable should be the independent variable and which should be the dependent variable.

b. Draw a scatter plot of the ordered pairs.

c. Calculate the least-squares line. Put the equation in the form of: y^{^} = a + bx.

d. Find the correlation coefficient. Is it significant?

e. Find the estimated maximum values for the restaurants on page ten and on page 70.

L Does it appear that the restaurants giving the maximum value are placed in the beginning of the "Fine Dining" section? How did you arrive at your answer?

g. Suppose that there were 200 pages of restaurants. What do you estimate to be the maximum value for a restaurant listed on page 200?

k. Is the least squares line valid for page 200? Why or why not?

i. What is the slope of the least-squares (best-fit) line? Interpret the slope.

Question 2 - Given

State	# letters in name	Year entered the Union	Rank for entering the Union	Area (square miles)
Alabama	7	1819	22	52,426
Colorado	8	1876	38	104,100
Hawaii	6	1959	50	10,932
Lowa	4	1845	29	56,276
Maryland	8	1788	7	12,407
Missouri	8	1821	24	69,709
New Jersey	9	1787	3	8,722
Ohio	4	1803	17	44,828
South Carolina	13	1788	8	32,008
Utah	4	1896	45	84,904
Wisconsin	9	1848	30	65,499

We are interested in whether or not the number of letters in a state name depends upon the year the state entered the Union.

a. Decide which variable should be the independent variable and which should be the dependent variable.

b. Draw a scatter plot of the data.

c. Does it appear from inspection that there is a relationship between the variables? Why or why not?

d. Calculate the least-squares line. Put the equation in the form of: y^{^} = a + bx.

e. Find the correlation coefficient. What does it imply about the significance of the relationship?

f. Find the estimated number of letters (to the nearest integer) a state would have if it entered the Union in 1900. Find the estimated number of letters a state would have if it entered the Union in 1940.

g. Does it appear that a line is the best way to fit the data? Why or why not?

h. Use the least-squares line to estimate the number of letters a new state that enters the Union this year would have. Can the least squares line be used to predict it? Why or why not?

Reference no: EM132243589

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