# Mathematics

1) Analyze the residual plot below and identify which, if any of the conditions for an adequate linear model is not met.

2

0

-2 5 15 25

(I cannot make the plots but they are below and above the middle line. There is one dot in conjunction of -2 and 5; one dot on the line of 15 and one on the above 25 located high of both previous. All other plots were everywhere that is how I can explain it)

Which of the conditions for an adequate linear model is not met?

A-Patterned residuals

B-None

C-Constant error variance

D-Outlier

2) Consider the data set given in the accompanying table. Complete parts (a through g)

X -2 -1 0 1 2

Y -2 0 2 3 5

a) Draw a scatter diagram treating x as the explanatory variable and y as the response variable. Choose the correct graph below.(please just make the correct draw and I will figure it out)

b) Fine the equation of the line containing the points (-2,-2) and (2,5). The equation of the line is y = (…….)x + (……).

c) Graph the line found in part (b) on the scatter diagram. Choose the correct graph below (Please make the right graph then I will figure it out).

d) Determine the least-squares regression line. Choose the correct answer.

A-the least-squares regression line is y = 1.5x + 1.75.

B-the least-squares regression line is y =1.7x + 1.75.

C-the least-squares regression line is y =1.7x + 1.6.

D-the least-squares regression line is y =1.6x + 1.7.

e) Graph the least-squares regression line on the scatter diagram. Choose the correct graph below.(Please graph the least squares line and I will figure it out).

f) Compute the sum of the squared residuals for the line found in part (b). The sum of the squared residuals for the line founds in the part (b) is (…..)

g) Compute the sum of the squared residuals for the least-squares regression line found in part (d). The sum of the squared residuals for least squares regression line is (……).

3) For the data set shown below, do the following. (a) Compute the standard error, the point estimate for σ. (b) Assuming the residuals are normally distributed, determine Sb1. (c) Assuming the residuals are normally distributed, test H0: β1=0 verses H1: β1≠0 at he a=0.05 level of significance.

X 20 30 40 50 60

Y 100 93 91 85 72

a) Determine the point estimate for σ. Se = (…….) (do not round until the final answer then round to four decimal places as needed).

b) Find the sample standard error of b1. Sb1 = (……)(Use the answer from part (a) to find this answer. Round to four decimal places as needed.)

c) Which of the following conclusions is correct?

A-Do not reject H0 and conclude that a linear relation exists between x and y.

B-Do not reject H0 and conclude that a linear relation does not exist between x and y.

C-Reject H0 and conclude that a linear relation does not exist between x and y.

D-Reject H0 and conclude that a linear relation exists between x and y.

4) Match the linear correlation coefficient to the scatter diagram. The scales on the x- and y- axis are the same for each scatter diagram.

(a) r= -0.969, (b) r= -1, (c) r= -0.049.

R

R

Reponse

I Exp II Exp III Explanatory

few dots between the 2 lines; many dots over the place in 2 lines; dots on the straight line.

A-Scatter diagram ( Ii/ I/ III)

B-Scatter diagram (II/ I/ III)

C-Scatter diagram (I/III/II)

5) A scatter diagram is shown to the right with one of the points drawn in blue. In addition, two least squares regression lines are drawn. The line drawn in red is the least squares regression line with the point in blue excluded. The line drawn in blue is the least squares regression line with the point in blue included. On the basis of these graphs, do you think the point in the blue is influential?

20 red line

response

15

10 blue line

5 10 15 Explanatory

(There are 5 dots above the blue and red line and 5 below red and blue line and three on the red and blue)

Does the point in the blue seem to be influential?

A-No

B-Yes

6) Because colas tend to replace healthier beverages and colas contain caffeine and phosphoric acid, researcher wanted to know weather consumption of colas is associated with lower bone mineral density in women. The data shown in the accompanying table represent the typical number of cans of soda consumed in a week and the bone mineral density of the femoral neck for a sample of 15 women. The data were collected through a prospective cohort study. Complete parts (a) through (f).

Number of Bone mineral

Colas per week density (g/cm2)

0 0.897

0 0.884

1 0.891

1 0.877

2 0.888

2 0.871

3 0.868

3 0.876

4 0.873

5 0.875

5 0.871

6 0.867

7 0.862

7 0.872

8 0.865

a) Find the leas squares regression line treating cola consumption per week as the explanatory variable. Choose the correct answer below.

A-The least squares regression line is ŷ= -0.0030x + 0.8866.

B- The least squares regression line is ŷ= 0.8866x – 0.0030.

C- The least squares regression line is ŷ= 0.0030x – 0.8866.

D- The least squares regression line is ŷ= -0.8866x + 0.0030.

b) Interpret the slope.

For each additional cola consumed per week, bone mineral density will (increase/decrease) by (0.0030; 1.0053; 0.5423; 0.8866) g/cm2, on average.

c) Interpret the intercept. Choose the correct answer below.

A-For each additional cola consumed per week, bone mineral density will decrease by 0.0030g/cm2, on average.

B-For a woman who does not drink cola, bone mineral density will be 0.030 g/cm2.

C-it is not appropriate to interpret the y-intercept. It is outside the scope of the model.

D-For a woman who does not drink cola, bone mineral density will be 0.8866 g/cm2.

d) Predict the bone mineral density of the femoral neck of a woman who consumes four cola per week.

The Predict value of the bone mineral density of the femoral neck of this woman is (……) g/cm2. (Round to four decimal places as needed)

e) The researcher found a woman who consumes of four colas per week to have a bone mineral density of 0.873 g/cm2. Is this woman’s bone mineral density above or below average among all women who consume four cola per week?

A-Above average

B-Below average

f) Would you recommend using the model found in part (a) to predict the bone mineral density of a woman who consumes two cans of cola per day?

A- No

B- Yes

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