Question

1. Given the following observations of quantitative variables
**X** and **Y**:

x= 0, 1, 2, 3, 15

y= 3, 4, 6, 10, 0

a. Make a scatterplot of the data on the axes. Circle the most influential observation. (4 points)

(b) Determine the LSRL of Y on X. Draw
this line carefully on your scatterplot. (4 points)

(c) What is the definition of a regression outlier? (4
points)

(d) Which data point is the biggest regression outlier?
**(4 points)**

(e) What is the residual at the point identified in part (c)? (4
points)

(f) Construct a residual plot for these data. (4
points)

(g) Interpret your residual plot, i.e., what does the residual
plot tell you? (4 points)

2. Anthropologists must often estimate from human remains how tall the person was when alive. Carla is studying how overall height can be predicted from the length of leg bone in a group of 36 living males. The data show that the bone lengths have mean 45.9 cm and standard deviation 4.2 cm, the overall heights have mean 172.7 cm and standard deviation 8.14 cm, and the correlation between bone length and height is 0.914.

(a) What is the slope of the LSRL of
height on bone length? (6 points)

(b) About what percent of the observed variation in the heights of the men can be explained by the linear regression of height on bone length? (4 points)

(c) Based on your answer to (b), how would you describe the goodness of linear fit? (4 points)

(d) Determine the equation of the LSRL of height on bone length. (4 points)

3. Consider the following scatterplot:

Provide an approximate equation for the regression line that has been drawn on the plot. (6 points)

Answer #1

a) This the scatter plot of Y and X

To find the most influential observation we will fit a trendline through this data. A trend line is a line which covers all data points or passes near them. In this case we have trend line as

Since it has to pass near all the observation we have to draw it like this. However if did not have the last data point(15,0) our trendline would be different. Here is the scattter plot without last point

The most influential observation is the one whose deletion from the dataset noticeably changes the result. Hence our most influential observation is (15,0).

b) This line which passes through all observations is called LSRL of Y on X.

c) Data points that diverge in a big way from the overall pattern of the data set are called Regression outlier. An influential point is also an example of Regression outlier.

d) Data Point (15,0) is the biggest oulier because none of the other X points are near 15 and no other Y point is near 0. Thus both (15,0) deviate from the whole data set (X,Y)

*Please give thumbs up to my
answer...!!*

Given are five observations for two variables, x and
y.
xi
1
2
3
4
5
yi
4
6
6
11
15
Which of the following scatter diagrams accurately represents
the data?
1.
2.
3.
What does the scatter diagram indicate about the relationship
between the two variables?
Develop the estimated regression equation by computing the the
slope and the y intercept of the estimated regression line
(to 1 decimal).
ŷ = + x
Use the estimated regression equation to...

Data Set:
x
y
0
4
2
2
2
0
5
-2
6
1
1. Find intercept b0
2. Find slope B1
3. Find the best fitted linear regression equation
4.Graph observations
5.Graph the linear equation on the same plot
6. Find the coefficient of Determination r²
7. Find the linear correlation coefficient r
8.Interpret r (the correlation between x & y)

Given are five observations for two variables, x and y.
X: 1 2 3 4 5
Y: 4 5 5 11 13
a. Try to approximate the relationship between x and y by
drawing a straight line through the data.
b. Develop the estimated regression equation by computing the
values of b0 and b1 (to 1 decimals).
y= _____ + ______x
c. Use the estimated regression equation to predict the value of
y when x=4 (to 1 decimals).
y=_____

A statistical program is recommended.
Consider the following data for two variables, x and
y.
xi
135
110
130
145
175
160
120
yi
145
105
120
115
130
130
110
(a)
Compute the standardized residuals for these data. (Round your
answers to two decimal places.)
xi
yi
Standardized
Residuals
135
145
110
105
130
120
145
115
175
130
160
130
120
110
Do the data include any outliers? Explain. (Round your answers
to two decimal places.)
The standardized...

2. When anthropologists study human skeletal remains,
an important piece of information is stature
(height). Since skeletons are often incomplete,
inferences about stature are based on statistical methods that
utilize small bones. The following data give the
relationship between metacarpal bone length and stature.
x, metacarpal length(cm) y, stature (cm)
45 171
51 178
39 157
41 163
52 183
48 172
49 183
46 172
What is the correlation coefficient, r? Does this
value of r suggest that the regression line is appropriate...

Consider the following data for two variables, x and
y.
xi
135
110
130
145
175
160
120
yi
145
105
120
115
130
130
110
(a)
Compute the standardized residuals for these data. (Round your
answers to two decimal places.)
xi
yi
Standardized
Residuals
135
145
110
105
130
120
145
115
175
130
160
130
120
110
Do the data include any outliers? Explain. (Round your answers
to two decimal places.)
The standardized residual with the largest absolute...

Given are five observations for two variables, x and
y.
xi
1
2
3
4
5
yi
2
8
6
11
13
a) Develop the estimated regression equation by computing the
values of b0 and
b1 using
b1 =
Σ(xi −
x)(yi −
y)
Σ(xi −
x)2
and b0 = y −
b1x.
ŷ =?
b) Use the estimated regression equation to predict the value of
y when
x = 2.

Data on the fuel consumption yy of a car at various speeds xx is
given. Fuel consumption is measured in mpg, and speed is measured
in miles per hour. Software tells us that the equation of the
least‑squares regression line
is^y=55.3286−0.02286xy^=55.3286−0.02286xUsing this equation, we can
add the residuals to the original data.
Speed
1010
2020
3030
4040
5050
6060
7070
8080
Fuel
38.138.1
54.054.0
68.468.4
63.663.6
60.560.5
55.455.4
50.650.6
43.843.8
Residual
−17.00−17.00
−0.87−0.87
13.7613.76
9.199.19
6.316.31
1.441.44
−3.13−3.13
−9.70−9.70
To...

Use the following information for problems 17-19:
Given the following data:
x
1
2
3
4
5
6
y
22
31
28
41
33
41
Which of the following would be the LSRL for the given data?
Determine the correlation coefficient for the data?
Find the residual value for x = 5.

Given are five observations for two variables, x and
y.
x i
1
2
3
4
5
y i
4
7
6
12
14
Round your answers to two decimal places.
a. Using the following equation:
Estimate the standard deviation of ŷ* when x =
4.
b. Using the following expression:
Develop a 95% confidence interval for the expected value of
y when x = 4.
to
c. Using the following equation:
Estimate the standard deviation of an individual value...

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