3) Data were collected to explain the amount of a customer's purchase (expressed in $'s) bused on the amount of time the customer has spent on the company's website (expressed in minutes) Complete the Table Below Regression Statistics Multiple R R Square Adjusted R Square 0.508 Standard Error Observations 12 ANOVA Significance F 0.005598142 df MS F Regression 63067.3 Residual 51086.4 Total Standard Error Upper 95% Coefficients t Stat P-value Lower 95% Intercept -3.53 42.21 0.935 Time 7.12 2.03 0.006

Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter7: Distance And Approximation
Section7.3: Least Squares Approximation
Problem 31EQ
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Data were collected to explain the amount of a customer’s purchase (expressed in $’s) based on the amount of time the customer has spent on the company’s website (expressed in minutes) *COMPLETE THE DATA TABLE BELOW*
f) To determine the predicted purchase amt for
a cUstomer who has spent
30 minutes
the website ?
the
results
The regression equation bafed
ニ -3.53+7,12x
ic purcha s
-3.53+1.12 time
Substitute time =30 in
the equation
Purchase =
-3.53+7.12 time
-3. 53+7,1230=~3,53+213,63
ニ
$210,07
Transcribed Image Text:f) To determine the predicted purchase amt for a cUstomer who has spent 30 minutes the website ? the results The regression equation bafed ニ -3.53+7,12x ic purcha s -3.53+1.12 time Substitute time =30 in the equation Purchase = -3.53+7.12 time -3. 53+7,1230=~3,53+213,63 ニ $210,07
3) Data were collected to explain the amount of a customer's purchase (expressed in $'s) based on the
amount of time the customer has spent on the company's website (expressed in minutes)
Complete the Table Below
Regression
Statistics
Multiple R
R Square
Adjusted R Square
Standard Error
0,508
Observations
12
ANOVA
Significance F
0.005598142
df
MS
F
63067.3
Regression
Residual
51086.4
Total
Standard
Error
Upper
95%
Coefficients
t Stat
P-value
Lower 95%
Intercept
-3.53
42.21
0.935
Time
7.12
2.03
0.006
Based on the regression results, answer the following questions
a) What is the estimated regression equation?
Intercept : -3,53
cst
reg equi
time = 7, 12
b) What percentage of the variation in purchase amount is explained by time?
STOpel here its time)
Y = -3,53+7,12X
Adjusted rquare
= 0.508
0,50X 100 '/
5o, 87,
c) What is the correlation between purchase amount and time?
R -Squared (R2) = 6.S0g
correlation (r) r=r=
correlatioa btwn purch
amount and
time
0.4127
r = 0, SG8
r =0. 17
d) What is the standard error of the error term in the regression equatiðn?'
SE =SSResidual
de - SI086,412-2=5108.64 =71,475
e) Is the coefficient on the variable “time" statistically significantly different than 0 at the 5% level of
significance? How do you know?
yes, the variable time
,s Sig dif from ø at S
Co rres
d= 0.05
Ievel
because the R-value
is less than Sig level
f) What is the predicted purchase amount for a customer who has spent 30 minutes on the website?
ing
Sig
is 0,.00c, which..
to time
5
Transcribed Image Text:3) Data were collected to explain the amount of a customer's purchase (expressed in $'s) based on the amount of time the customer has spent on the company's website (expressed in minutes) Complete the Table Below Regression Statistics Multiple R R Square Adjusted R Square Standard Error 0,508 Observations 12 ANOVA Significance F 0.005598142 df MS F 63067.3 Regression Residual 51086.4 Total Standard Error Upper 95% Coefficients t Stat P-value Lower 95% Intercept -3.53 42.21 0.935 Time 7.12 2.03 0.006 Based on the regression results, answer the following questions a) What is the estimated regression equation? Intercept : -3,53 cst reg equi time = 7, 12 b) What percentage of the variation in purchase amount is explained by time? STOpel here its time) Y = -3,53+7,12X Adjusted rquare = 0.508 0,50X 100 '/ 5o, 87, c) What is the correlation between purchase amount and time? R -Squared (R2) = 6.S0g correlation (r) r=r= correlatioa btwn purch amount and time 0.4127 r = 0, SG8 r =0. 17 d) What is the standard error of the error term in the regression equatiðn?' SE =SSResidual de - SI086,412-2=5108.64 =71,475 e) Is the coefficient on the variable “time" statistically significantly different than 0 at the 5% level of significance? How do you know? yes, the variable time ,s Sig dif from ø at S Co rres d= 0.05 Ievel because the R-value is less than Sig level f) What is the predicted purchase amount for a customer who has spent 30 minutes on the website? ing Sig is 0,.00c, which.. to time 5
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