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Unformatted text preview: Offline HW #9 — Chapter 15 I When additional independent variables are added to a simple linear regression, the coefﬁcient of determination R2
may ' become negative . increase or stay the same decrease or stay the same 5;. stay the same 2.. A real estate analyst haggeyELOPeq‘a multiple regression line, y = 60 + 0.068 x1  2.5 X2, to predict y = the
market price of a hometh \$1,0005D using independent variables, x1 = the total number of square feet of living
space, and X2 = the age of‘fh'é‘hb‘Gs'é in years. The regression coefﬁcient of x1 suggests this: , The addition of 1 square foot area of living space results in a predicted increase of $0.068 in the price of the
home if the age of the home were held constant. K‘ The addition of 1 square foot area of living space results in a predicted increase of $0.068 in the price of the
home for homes of different ages. Q §0Q%\fi OO‘\ 7‘. The addition of 1 square foot area of living space results in a predicted increase of $68.00 in the price of the
home if the age of the home were held constant. The addition of 1 square foot area of living space results in a predicted increase of $68.00 in the price of the
home with the age of the home allowed to vary. V C USE F TEST
3. The test statistic used to test the verall significance of a multiple regression model, the null hypothesis that each one the B—coefficients of the xvariables in the model is equal to zero, is tested against the alternative hypothesis that at least one the 8coefficients of the xvan’ables in the model is at zero, is the .' Fvalue from the Fdistn‘bution tables 22 )(2 statistic 
F _ nsg ntcatgmih g. F value calculated as mean square regression divided b mean 5 a e
V q” r em” Msuzsmvnt ERROR\ .’ t statistic u , To test if an individual 3, coefﬁcient in the population multiple regression model is significantly different from zero, a hypothesis test is conducted on the corresponding b; coefﬁcient in the regression equation developed using
sampie data. This test is a H I 3.: Q vs. Maggie t test 0 \ S
§‘ ' \_ (OE ’
T = V 0
nonparametric test 55 (OEF z—test .1, . F—test III The following is a partial computer output of a multiple regression analysis of a data set containing {cgsets of observations on the dependent variable, SALES (
variables, ADVT (= advertising expenditure in th = sales volume in thousands of dollars), and two independent
ousands of dollars) and REPS (= number of sales representatives). Predictor Coef SE Coef Constant 7.017 5.316 ADVT 8.623 2.396 REPS 0.086 0.184 Analysis of Variance Source DF SS MS Regression 2 321.11 160.55 Residual Error 7 63.39 9.05 22'... .2 m J 9 3845“ w number of sales representatives constant? $17, 246
$17.25 ‘; $1,724,600
$8.26 1 $8623 A
SRLES = “Lon + tunimﬁ + magnum} iv  What is the numerical value of R2? 100.00% 3'» f' 98.75% g 83.51% 77.72% I 78.79% k
A SALES
. a
5 mm  3.9.3:? exni’xoochzmjm
58R 3M.“
3*: = K
R SET “”0 a 33. 1'7, '1 What is the standard error of the estimate? r.
_v 6.23
1.72
3.00
8.26 0.24 i; .What is the critical or table F
17.73 ,.
.v f: 8.26 8.02 , A. 7.05 g. 9.55 SSC Ramon EMMA 4m
7'” 2 1i value in the test of the overall model at a 0.01 level of significance? A. q. In a regression study, a multiple regression model with two explanatory variables is developed using a data set
with 23 observations. In the ANOVA table for this model, the sum of squares total (SSW) is = 12500 and the sum
0 squares regression (SSR) = 9500. The F—value for the test of the overall signiﬁcance of this model is 1.32  Hm .ﬂsLL... ‘i'lsg =3 (.7
 F MSE (50 1:0 L 1‘; 413.04 6/
. 535 : SST ~SSK = iu‘oo “1500 = 3000 22
: S§§ _ 3000
g, 31.67 =? ﬂSE rmAxl  W : lSO in. In a regression study, a multiple regression model with two explanatory variables is developed using a data set
with 23 observations. In the ANOVA table for this model, the sum of squares total (SSW) is = 12500 and the sum of squares error (SSE) = 3000. The coefficient of multiple determination (R2) is 0.58 38‘ = SST SSE = llsoo mug“ : “0°
’2 0.24
x, SSK  9S0!) 
T") 132 K ‘ SST (1.506 . ‘7‘ 767°
. 0.76
{An ii. In a regression study, a multiple regression model with two explanatory variables is developed using a data set
with 23 observations. In the ANOVA table for this model, the sum of squares total (SSW) is = 12500 and the sum of squares error (SSE) = 3000. The standard error of estimate (se) is 311.96
dad
g. 12.25 . 3).” = [50 “1.1le
g 20 ”Q n
r; 150 II In a multiple regression analysis the numerical value of the adjusted R2 is always greater than that of the coefﬁcient of multiple determination (R2) “61¢: ° PHCE I: — I). 3‘ always less than that of the coefﬁcient of multiple determination (R2) at < “L
s. 5.) never less than that of the coefﬁcient of multiple determination (R2) always equal to that of the coefﬁcient of multiple determination (R2) l3. As n, the number of observations in the data set increasesJ the gap between R2 and adjusted R2 . . (KL SXR ‘_ SSE
increases . SST *5“
remains the same
1 __ m. “ . SSE N L “K
gets multiplied byn " R“ = ‘ nickl ‘31 ». R HS m. RERSIS QEtSdeed by" AS m rucamstx) 'rilrS FACTOR. nPfRo actits \ g decreases N , A multiple regression analysis produced the following tables.
_ mm... 121783 60891.48 14.76117 0.000286
61m 4125.112 —
_ v
m~l8¢= .. , The regression equation for this analysis is y = 6166849 + 3.33833 x1 + 1.780075 X:
r'. y = 154.5535 4» 2.333548 x1 + 0.335605 x;
3‘. y = 154.5535 _ 1.43058 X1 + 5.30407 x2 f‘; y = 616.6849  3.33833 x1 ~ 1.780075 xz g; y = 616.6849  3.33833 X1 + 1.780075 X2 5. The sample size for this analysis is 17
r 34
19
‘0! 18
."« 15 4.. Using 01 = 0.01 to test the null hypothesis Ho: 8 1 = 3 2 = O, the critical Fvalue is . 3!. —‘F {hf/NA” 8.40 ‘u  “”311”
.’", 6.11
3.36
1;. 8.68
g. 6.36 41. Using 01 = 0.05 to test the null hypothesis Ho: 31 = 0, the critical t value is . C m isonwaae, 11.: e, in 12.110
11.740 .4 12500 3 USE kw“ "V‘v‘ g. 12.131 : 803‘s": 1' 1.13] i 1.753 Is" The following ANOVA table is from a multiple regression analysis with n = 35 and four independent variables. 1&3..le k. The number of degrees of freedom for regression is A" = H
g 4
30
’ , 35
'_ 1
r“. 34 33 K _ f) 0 Q
o The MSR value is L. "l
b. The number of degrees of freedom for error is (7" 1k" \ . _
_ 233.33 : Wk
35 ' 3X  \l \ x
175.00
K". 1 1 30 t
350.00
1', 34 .
5'. 275.00
C} 4 
700.00
a 30 ‘
.33....
(w The MSE value is LL. 0‘. The observed Fvalue is
g, 75.00 , 3.9L 0.43 F . H33 _ i7:
5;. 20.00 30 g. 17.50 w l0
8.82 1', 0.50 = i7. $0
8.57 0.70
3? 10.00 ' 2.33
I. . The value of the standard error of the estimate Se is
13.23
  xx:
10.00 A e In“ A» ~\
.. 3.16
 300 ‘ 
(x 17.32  “I”  3.“).
_, 1 d
C} 26.46
3“ i _m_a‘_l._. iii...
.6. The R2 value is S§ T . I The adjusted R2 value is &‘ ”\ XST
0.66 : 70° 0.70 .. ‘ 3'4 so 0
0 II — o
0.76 lo 1 0.80 3° ”0°
3 70 o z 7
0.30 0.76 “x 5 (6 7o
0 . 80 f; 0 . 30 0.70 n 0.66
§ 1, S 7 ﬂ “oiﬁig‘ﬁx’ 912%“) W H '11 Linn on! V“ it. Consider the multiple regression output shown below: Do NOT REIEST Analysis of Variance tool: DNR Ho Source DF 55 MS F P Regression 4 3397.7 849.4 3.55 0.029 7 . oi: DNR bio
Residual Error 15 3493.1 232.9 Total 19 68908 < . 05 =9 REWEC" “o What conclusion can be reached about this regression model from this output?
.’ At alpha = .001, at least one of the regression coefﬁcients is different from zero.
7', At alpha = .01, at least one of the regression coefﬁcients is different from zero.
3‘. None of the regression coefﬁcients are different from zero. g, At alpha = .05, at least one of the regression coefﬁcients is different from zero. ...
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 Fall '08
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