Home
Collaborative statistics using Bivariate descriptive statistics Bivariate descriptive statistics
The following are advertised sale prices of color televisions at Anderson’s.
Size (inches)
Sale Price ($)
9
147
20
197
27
297
31
447
35
1177
40
2177
60
2497
a Decide which variable should be the independent variable and which should be the dependent variable.
b Make 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
size 12{y=a+ ital "bx"} {}
e Find the correlation coefficient. Is it significant?
f Find the estimated sale price for a 32 inch television. Find the cost for a 50 inch television.
g Use the two points in (f) to plot the least squares line on your graph from (b).
h Does it appear that a line is the best way to fit the data? Why or why not?
i Are there any outliers in the above data?
j What is the slope of the least squares (best-fit) line? Interpret the slope.
Below are the average heights for American boys. (Source:
Physician’s Handbook, 1990 )
Age (years)
Height (cm)
birth
50.8
2
83.8
3
91.4
5
106.6
7
119.3
10
137.1
14
157.5
a Decide which variable should be the independent variable and which should be the dependent variable.
b Make 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
size 12{y=a+ ital "bx"} {}
e Find the correlation coefficient. Is it significant?
f Find the estimated average height for a one year–old. Find the estimated average height for an eleven year–old.
g Use the two points in (f) to plot the least squares line on your graph from (b).
h Does it appear that a line is the best way to fit the data? Why or why not?
i Are there any outliers in the above data?
j Use the least squares line to estimate the average height for a sixty–two year–old man. Do you think that your answer is reasonable? Why or why not?
k What is the slope of the least squares (best-fit) line? Interpret the slope.
c Yes
d
y
^
=
65
.
0876
+
7
.
0948
x
size 12{y="65" "." "0876"+7 "." "0948"x} {}
e 0.9761; yes
f 72.2 cm; 143.13 cm
h Yes
i No
j 505.0 cm; No
k slope = 7.0948. As the age of an American boy increases by one year, the average height tends to increase by 7.0948 cm.
The following chart gives the gold medal times for every other Summer Olympics for the women’s 100 meter freestyle (swimming).
Year
Time (seconds)
1912
82.2
1924
72.4
1932
66.8
1952
66.8
1960
61.2
1968
60.0
1976
55.65
1984
55.92
1992
54.64
2000
53.8
2008
53.1
a Decide which variable should be the independent variable and which should be the dependent variable.
b Make 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
size 12{y=a+ ital "bx"} {}
e Find the correlation coefficient. Is the decrease in times significant?
f Find the estimated gold medal time for 1932. Find the estimated time for 1984.
g Why are the answers from (f) different from the chart values?
h Use the two points in (f) to plot the least squares line on your graph from (b).
i Does it appear that a line is the best way to fit the data? Why or why not?
j Use the least squares line to estimate the gold medal time for the next Summer Olympics. Do you think that your answer is reasonable? Why or why not?
Source:
OpenStax, Collaborative statistics using spreadsheets. OpenStax CNX. Jan 05, 2016 Download for free at http://legacy.cnx.org/content/col11521/1.23
Google Play and the Google Play logo are trademarks of Google Inc.
