Question

1.

Management of a fast-food chain proposed the following regression model to predict sales at outlets:

*y = β _{0} + β_{1}x_{1} +
β_{2}x_{2} + β_{3}x_{3} + ε*,
where

*y =* sales ($1000s)

*x _{1}*= number of

*x _{2}*=

*x _{3}*is 1 if a

The following estimated regression equation was developed after 20 outlets were surveyed:

**= 12.6 − 3.6 x_{1}+
7.0x_{2}+ 14.1x_{3}**

Use this equation to predict sales for a store with 4
competitors, a population of 4300 within one mile, and a drive-up
window;

**round your answer to two decimal places and omit the $
symbol.**

**2.**

You have run a simple regression on a sample with 21 observations, and obtained the following information:

SSR = 233

SST = 354

**Calculate the value of the standard error of estimate,
s**

**Round your answer to three decimal places**

**3. **

For a data set with *n* = 26 observations and *k*
= 6 independent variables, use F-table to find the **critical
value** for a test of overall significance with α = 2.5%

**Show your answer with four decimal places.**

Answer #1

Management of a fast-food chain proposed the following
regression model to predict sales at outlets:
y = β0 + β1x1 +
β2x2 + β3x3 + ε,
where
y = sales ($1000s)
x1= number of competitors
within one mile
x2= population (in 1000s)
within one mile
x3is 1 if a drive-up window
is present, 0 otherwise
Multiple regression analysis was performed on a random sample of
data collected from 25 outlets.
Given the following portion of an output of the regression...

Question #1
The sale of handguns is very popular in the Hill Country. A
Criminal Justician researcher who has been investigating the
prevalence of guns in the State came up with the following
regression model to predict sales at one of the gun outlets.
where
X1 = number of competitors who also sell
guns within one mile
X2 = population within 1 mile (1000s)
X3= {=1 when purchase by drive-up window is
allowed; =0 when purchase by drive-up window is...

The following
regression model has been proposed to predict sales at a computer
store:
y_hat = 50 –
3x1 + 20x2 +
10x3
where
x1
= competitor's previous day's sales (in $1000s)
x2
= population within 1 mile (in 1000s)
x3
= 1 if any radio advertising was used and 0
otherwise.
y_hat= sales (in
$1000s)
Predict the change in
sales (in dollars) when radio advertising was used, all else
constant.
This, is from question one if needed; Predict sales (in...

8. Consider the following data for a dependent variable
y and two independent variables, x1 and
x2.
x1
x2
y
30
12
94
47
10
108
25
17
112
51
16
178
40
5
94
51
19
175
74
7
170
36
12
117
59
13
142
76
16
211
(a) Develop an estimated regression equation relating y
to x1. (Round your numerical values to one decimal
place.)
ŷ = ______
Predict y if x1 = 51. (Round
your answer...

The owner of a movie theater company used multiple regression
analysis to predict gross revenue (y) as a
function of television advertising
(x1) and newspaper advertising
(x2).The estimated regression equation
was
ŷ = 83.1 + 2.23x1 +
1.30x2.
The computer solution, based on a sample of eight weeks,
provided SST = 25.4 and SSR = 23.395.
(a) Compute and interpret R2 and
Ra2.
(Round your answers to three decimal places.)
The proportion of the variability in the dependent variable that...

1, As a result of running a simple regression on a data set, the
following estimated regression equation was obtained:
= 1.6 −
3.0x
Furthermore, it is known that SSR = 674, and SSE = 128.
Calculate the correlation coefficient R ; round
your answer to three decimal places.
2.
A sample of data with n = 22 observations is used to run a
multiple regression with 8 independent
variables.
If this data set has SST = 2309.1068 and SSE...

We give JMP output of regression analysis. Above output we give
the regression model and the number of observations, n,
used to perform the regression analysis under consideration. Using
the model, sample size n, and output:
Model: y = β0 +
β1x1 +
β2x2 +
β3x3 +
ε Sample size:
n = 30
Summary of Fit
RSquare
0.956255
RSquare Adj
0.951207
Root Mean Square Error
0.240340
Mean of Response
8.382667
Observations (or Sum Wgts)
30
Analysis of Variance
Source
df
Sum...

Regression Analysis with a Minitab output
Assume that your company owns multiple retail outlets in cities
across the United States. You conduct a study to determine if daily
sales levels (in hundreds of dollars) can be predicted by the
number of competitors that are located within a one-mile radius of
each location and city population (in thousands of people).
Therefore, the dependent variable is SALES and the two independent
variables are NUMBER OF COMPETITORS and CITY POPULATION. Your
research team...

A sales manager collected the following data on x =
years of experience and y = annual sales ($1,000s). The
estimated regression equation for these data is
ŷ = 80 + 4x.
Salesperson
Years of
Experience
Annual Sales
($1,000s)
1
1
80
2
3
97
3
4
92
4
4
107
5
6
103
6
8
101
7
10
119
8
10
118
9
11
127
10
13
136
A. Compute SST, SSR, and SSE.
B. Compute the coefficient of...

In a regression analysis involving 30 observations, the
following estimated regression equation was obtained.
ŷ = 17.6 + 3.8x1 −
2.3x2 +
7.6x3 +
2.7x4
For this estimated regression equation, SST = 1,835 and SSR =
1,800.
(a)At α = 0.05, test the significance of the
relationship among the variables.State the null and alternative
hypotheses.
-H0: One or more of the parameters is not
equal to zero.
Ha: β0 =
β1 = β2 =
β3 = β4 = 0
-H0:...

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