Question

Simple regression analysis

The following data were collected to study the relationship between
the sale price, y and the total appraised value, x, of a
residential property located in an upscale neighborhood.

Property |
x |
y |
x2 |
y2 |
xy |

1 |
2 |
2 |
4 |
4 |
4 |

2 |
3 |
5 |
9 |
25 |
15 |

3 |
4 |
7 |
16 |
49 |
28 |

4 |
5 |
10 |
25 |
100 |
50 |

5 |
6 |
11 |
36 |
121 |
66 |

Draw a scatter diagram of the sale price and the total appraised
values

Calculate the Pearson’s coefficient of correlation, r

Describe the relationship between the sale price and the total appraised value

Find a regression equation of the sale price based on the total appraised value

Predict the sale price if the sale price and the total appraised value is 3.

Answer #1

Scatter plot with regression line

Perfect positive correlation between x and y

for x= 3 predicted price given by

y=-2.2+2.3*(3)=-2.2+6.9=4.7

The following data were collected to study a relationship
between time spent for training and an aptitude test score. (X =
months spent for training, Y = test score).
X
1
3
5.5
2
3.5
5
6
7
Y
2.5
4.5
6.7
3.5
4
5.2
6.5
6.8
Plot the data on a scatter diagram. Does it suggest
positive/negative relationship?
Find the sample correlation coefficient and test its
significance.
Write an equation of the regreesion line.
Estimate the value of the...

The following data have to do with the relationship between
maternal smoking (# of cigarettes smoked per day,
which is variable X) and infant birth weight (which is variable
Y). (∑X, ∑X2, ∑Y, ∑Y2, and ∑XY have
already been
calculated for you and are shown below in red
font.)
Cigarettes Per Day (X) X2 Infant
Birth Weight (Y) Y2 XY
2 4 7.5 56.25 15.0
6 36 7.2 51.84 43.2
10
100 6.9 47.61 69.0
12 144 6.2 38.44 74.4
14
196 5.8 33.64 81.2
∑X =
44 ∑X2
=
480 ∑Y
=
33.6 ∑Y2
=...

Given are five observations collected in a regression study on
two variables.
xi
2
6
9
13
20
yi
9
18
8
25
21
(a)
Develop a scatter diagram for these data.
A scatter diagram has 5 points plotted on it. The horizontal
axis ranges from 0 to 25 and is labeled: x. The vertical
axis ranges from 0 to 30 and is labeled: y. The points are
plotted from left to right in a downward, diagonal direction
starting in...

1. You are given the following data to fit a simple linear
regression x 1 2 3 4 5 y -2 4 2 -1 0 Using linear least squares,
determine the t-value for testing the hypothesis that no linear
relationship exist between y and x. (a) 0.01, (b) 0.03, (c) 0.09,
(d) 0.11, (e) 0.13

The following table is the output of simple linear regression
analysis. Note that in the lower right hand corner of the output we
give (in parentheses) the number of observations, n, used
to perform the regression analysis and the t statistic for
testing H0: β1 = 0 versus
Ha: β1 ≠ 0.
ANOVA
df
SS
MS
F
Significance F
Regression
1
61,091.6455
61,091.6455
.69
.4259
Residual
10
886,599.2711
88,659.9271
Total
11
947,690.9167
(n = 12;...

The following data have been collected for a simple linear
regression analysis relating sales (y) to price (x):
x
y
Price
($)
Sales
(units)
4
120
7
60
5
100
8
80
In applying the least squares criterion, the slope (b) and the
intercept (a) for the best-fitting line are b = -12 and a = 162.
You are to conduct a hypothesis test to determine whether you can
reject the null hypothesis that the population slope, β, is 0...

9.17 Data were collected for a random variable Y as a function
of another
random variable X. The recorded (x, y) pairs are as follows:
(3, 2) , (5, 3) , (6, 4) , (8, 6) , (9, 5) , (11, 8)
a. Plot the scatter diagram for these data.
b. Find the linear regression line of y on x that best fits these
data.
c. Estimate the value of y when x=15.

Suppose that a researcher collected the following set of data
on years of education (X) and number of children for a sample of
married adults:
X
Y
12
2
14
1
17
0
10
3
8
5
9
3
12
4
14
2
18
0
16
2
Draw a scatter plot of the data.
Write out the regression equation, then calculate and
interpret the meaning of the...

The commercial division of a real estate firm is
conducting a regression analysis of the relationship between
x, annual gross rents (in thousands of dollars), and
y, selling price (in thousands of dollars) for apartment
buildings. Data were collected on several properties recently sold
and the following computer output was obtained.
The regression equation is
Y = 20.0 + 7.27 X
Predictor
Coef
SE Coef
T
Constant
20.000
3.2213
6.21
X
7.270
1.3626
5.29
Analysis of Variance
SOURCE
DF
SS...

The commercial division of a real estate firm is conducting a
regression analysis of the relationship between x, annual
gross rents (in thousands of dollars), and y, selling
price (in thousands of dollars) for apartment buildings. Data were
collected on several properties recently sold and the following
computer output was obtained.
The regression equation is
Y = 20.0 + 7.26 X
Predictor
Coef
SE Coef
T
Constant
20.000
3.2213
6.21
X
7.260
1.3625
5.29
Analysis of Variance
SOURCE
DF
SS...

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