(a) Write the regression equation. ŷ= -11.320 +0.788x₁ +0.151x2 ✓ (b) Interpret the coefficients of the estimated regression equation found in part (a). (Give your answers in dollars.) As advertising increases by 1 unit ($1,000), sales are expected to increase by $ 788 to increase by $ 151 x when advertising is held constant. (c) At a = 0.05, test for the significance of the coefficient of advertising. State the null and alternative hypotheses. (Enter != for as needed.) 0 Ho x when the number of salespeople is held constant. As the number of salespeople increases by 1, sales are expected

Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter1: Functions
Section1.CR: Chapter 1 Review
Problem 86CR
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The following is part of the results of a regression analysis involving sales (y in millions of dollars), advertising expenditures (x, in thousands of dollars), and number of salespeople (x₂) for a corporation. The regression
was performed on a sample of 10 observations.
Constant
X1
x2
Ho:
55°F
Heavy sleet
(a) Write the regression equation.
Ha
Coefficients
-11.320
ŷ = -11.320+0.788x1 +0.151x2
0.788
2
0.151
=
Standard Error
(b) Interpret the coefficients of the estimated regression equation found in part (a). (Give your answers in dollars.)
As advertising increases by 1 unit ($1,000), sales are expected to increase by $ 788
to increase by $ 151
X when advertising is held constant.
(c) At a = 0.05, test for the significance of the coefficient of advertising.
State the null and alternative hypotheses. (Enter != for # as needed.)
B₁ = 0
B₁!=0
Find the value of the test statistic. (Round your answer to two decimal places.)
2.61
3
20.452
0.302
Find the p-value. (Round your answer to four decimal places.)
p-value .0349
State your conclusion.
F4 --
0.218
4
-Responses/submit/dep=30597856&tags=autosave#question4806908_11
%
5
6
17
&
7
fa
fo
X when the number of salespeople is held constant. As the number of salespeople increases by 1, sales are expected
8
DII
f10
DDI
12 insert
P
A
prt sc
[
backspace
home
num
lock
end
F
11:00 PM
11/29/2022
7
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pg up
004
Transcribed Image Text:esc You may need to use the appropriate technology to answer this question. The following is part of the results of a regression analysis involving sales (y in millions of dollars), advertising expenditures (x, in thousands of dollars), and number of salespeople (x₂) for a corporation. The regression was performed on a sample of 10 observations. Constant X1 x2 Ho: 55°F Heavy sleet (a) Write the regression equation. Ha Coefficients -11.320 ŷ = -11.320+0.788x1 +0.151x2 0.788 2 0.151 = Standard Error (b) Interpret the coefficients of the estimated regression equation found in part (a). (Give your answers in dollars.) As advertising increases by 1 unit ($1,000), sales are expected to increase by $ 788 to increase by $ 151 X when advertising is held constant. (c) At a = 0.05, test for the significance of the coefficient of advertising. State the null and alternative hypotheses. (Enter != for # as needed.) B₁ = 0 B₁!=0 Find the value of the test statistic. (Round your answer to two decimal places.) 2.61 3 20.452 0.302 Find the p-value. (Round your answer to four decimal places.) p-value .0349 State your conclusion. F4 -- 0.218 4 -Responses/submit/dep=30597856&tags=autosave#question4806908_11 % 5 6 17 & 7 fa fo X when the number of salespeople is held constant. As the number of salespeople increases by 1, sales are expected 8 DII f10 DDI 12 insert P A prt sc [ backspace home num lock end F 11:00 PM 11/29/2022 7 home pg up 004
(d) At a = 0.05, test for the significance of the coefficient of number of salespeople.
State the null and alternative hypotheses. (Enter != for # as needed.)
B₂=0
ß₂!= 0
Ho
Ha
Find the value of the test statistic. (Round your answer to two decimal places.)
69
Find the p-value. (Round your answer to four decimal places.)
p-value = .5097
X
State your conclusion.
O Reject Ho. There is sufficient evidence to conclude that B₂ is significant.
O Do not reject Ho. There is insufficient evidence to conclude that , is significant.
O Reject Ho. There is insufficient evidence to conclude that is significant.
O Do not reject Ho. There is sufficient evidence to conclude that B₂ is significant.
(e) If the company uses $48,000 in advertisement and has 790 salespeople, what are the expected sales? Give your answer in dollars.
$37931.97
X
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55°F
Heavy sleet
Read It
2
hp
□
W
Transcribed Image Text:(d) At a = 0.05, test for the significance of the coefficient of number of salespeople. State the null and alternative hypotheses. (Enter != for # as needed.) B₂=0 ß₂!= 0 Ho Ha Find the value of the test statistic. (Round your answer to two decimal places.) 69 Find the p-value. (Round your answer to four decimal places.) p-value = .5097 X State your conclusion. O Reject Ho. There is sufficient evidence to conclude that B₂ is significant. O Do not reject Ho. There is insufficient evidence to conclude that , is significant. O Reject Ho. There is insufficient evidence to conclude that is significant. O Do not reject Ho. There is sufficient evidence to conclude that B₂ is significant. (e) If the company uses $48,000 in advertisement and has 790 salespeople, what are the expected sales? Give your answer in dollars. $37931.97 X Need Help? Submit Answer 55°F Heavy sleet Read It 2 hp □ W
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