WORKSHEET - REGRESSION
The table below displays data on the temperature (OF) reached on a given day and the
number of cans of soft drink sold from a particular vending machine in front of a grocery
store.
temperature
quantity
X = 85.3,
75
31
70
30
Y = 46.46,
80
40
90
52
93
57
s; = 107.09,
98
59
s~
=
72
33
75
38
75
32
80
45
90
53
95
56
15
2: (Xi
131.6952,
i=1
- X)(Yi - y)
98
62
=
91
51
98
58
n-;o
S')c. ;:: 1-~Z. I
1627.667
1. Identify the explanatory variable (x) and the response variable (y).
explanatory variable:
response variable:
=
~--L.~
~ kOt..L --h,'
b
l~
i loiP1
Sf :; YL?>l.~
~d
2. Compute the correlation coefficient r.
r=
~ - ~ (x i -x)(:J i -
5)
.--L
I~
-­
S'x. ~ S:J-
~
\b;l.i. bb(
Y/0"1.09 * f 1"?>I.b95i
I
O.42fl &4
*'
3. Based on the computed value of r, what can you say about the association between
the temperature and the number of soft drinks sold.
'DaR\., -h'O-e,.
I
O-Md
S~
-J
~9u.~p
U~r
A
9\~ .. ,f{j
~F~ a... cl
~d
4. Compute the slope b for the least squares regression line.
l\.4158
S.::J
-Sx..
10,34-84
..
5. Provide an interpretation of the slope within the context of the problem.
~r ~ ~-h'O~ .i. ~ ilACM'.~
~F-n...te.> ~ ~oJectl t1.u....~
ILL(A.eQ..oeo
6. Compute the intercept a for the least squares regression line.
Ct;::
'i - b X
-)
a..
=
46.4-b -
IIA-
~
ef
S~~
bJ l.o8.5b,
Q...u.S
....j
l.ogSb *-~s.
- - 4'" ,\11;1..
a
7. Provide an interpretation of the intercept within the context of the problem.
=fi;( 0° -F J ~ \.t?~ cJ.e-o\ , ~~
~~ Lro\.&et ~ -4b. l( -teu.s
~u..Q
8. State the least
olee-o ~t- ~ a
square~gressiOnline.
ef
~S
ik+ec~t-
~~~
ilA.-~ta....4l0""-.
{.08b X-'
9. For a temperature of 85°F, predict how many cans of soft drinks will be sold.
S: - 4la.l'\
10. Can you predict the number of soft drinks being sold for a temperature of 62°F? Ex­
plain why or why not!
P1b!oa..b~ "=~..J -1-€... i s ~ &. ~
~u.e.
We
~
~-ht..
ilk -t-€t.'.s
11. Compute the residual for for the predicted values based on x
><: 12.:
S
'= -
4b. ,-, l + 1.0&6 •
><== ~l: C1 .. - 4lo. nl
~
16(
~
>C'.
= 72 and x = 91.
12 : 32..02..1
S
-:~ ~i~ ~ ~ -
e.<2- ~1?~ -ho u.
~ 33 -32.. 0 21 :
0.9.:1
te&\·~
1rlvhat does the residual plot suggest about the adequacy of the fi~ted simple linear = 5\ _ 52. bS5
+ 1.0gb" 9\ - 52.'=:,SS-
#=/
regression model? Explain.
.
-::. - 1.655
6
~ 2
.
""0
"Cij
&! -2
•
•
•
•
•
••
-6
65
70
75
80
•
ii
85
9'0
•
• •
•
95
100
temperature
13. Compute the coefficient of determination and give an interpretation the coefficient of
2.
r :
Q;uAs
determination. 2.
(0 ~(<sc:;-)
::: O· ICf 5 ~ 2.
45· 82 % .J
-;> \kU"\a..9I,'~ i lA. +a..ct
7\-bo~ 4-
~
-tv=- -of
~ C2uL be ~ ~ ~ ~ikct lA~
~01A.. ~~ ~~ ~ --fa,;
endrsi-~ ~~.