Cleveland Clothing Store is interested in investing in advertising to increase t

Question

Cleveland Clothing Store is interested in investing in advertising to increase their sales. They consider 4 different channels of advertisement: TV, radio, print, and other (i.e. social media). They want to find the relationship between the amount spent in each advertisement type and the sales amount.They take measurements for 18 days and the data is given below:

1) Find the least squares prediction equation where the sales is the dependent variable and the amount of investments in TV, radio, print, and other type of advertisements as the independent variables.(4 decimal points)

b0=

b1=

b2

b3=

b4=

3) Is the overall regression model significant? (Is at least one of the population regression parameters significant?)

H0: (Click to select)0 = 1= 2= 3= 4=01= 2= 3= 41= 2= 3= 4=0

Ha: At least one of 1, 2,…, 4 0

p-value: (2 decimal points)

At/With 95% confidence we (Click to select)cannotcan conclude that the overall regression relationship between the amount of investment in TV, the amount of investment in radio, the amount of investment in print, the amount of investment in other type of advertisements and the sales amount is significant.

This means (Click to select)at least one of the population regression parametersnone of the population regression parameters is/are not zero.

4) Test the significance of the following independent variables

a) Testing the significance of the amount of investment in TV advertisements

p-value: (4 decimals)

At/With 95% confidence we (Click to select)cannotcan conclude that the population regression parameter 1 is not zero.(The population parameter for TV advertisements is (Click to select)not significantsignificant. )

b) Testing the significance of the amount of investment in radio advertisements

p-value: (4 decimals)

We have (Click to select)somestrongvery strongextremely strong evidence that the relationship between the amount of investment in radio advertisement and the sales amount is significant.

c) Testing the significance of other type of advertisements

At/With 95% confidence we (Click to select)cancannot conclude that the population regression parameter 3 is not zero.(The population parameter other type of advertisements is (Click to select)not significantsignificant. )

5) After the number of independent variables and the sample size accounted for, what percentage of the variation in sales is explained by the amount of investments in TV, radio, print and other type of advertisements?

% (1 decimal)

6) "The mean sales for all possible scenarios with x1=50, x2=40,x3=10,x4=6 is between $13,911.8 and $22,752.4". This statement is explaining (Click to select)prediction interval.confidence interval. .

$1000s $1000s $1000s $1000s $1000s Row sales tv radio print other 1 18.4 48.4 34.9 14.9 8.4 2 21.8 55.4 23.8 12.1 9.7 3 21.6 56.6 20.6 11.9 7.9 4 33.8 61.6 14.1 17.5 9.9 5 20.9 49.4 28.6 10.9 8 6 15.9 47.4 27.9 12.4 7.9 7 49.5 72.8 43.4 13.1 11.4 8 26.7 59.9 13.7 14.7 9.8 9 28.7 58.3 27.3 9.8 9.1 10 19.7 51.8 22.9 21.1 8.8 11 45.8 65.1 39 29.4 12.3 12 54.4 68.2 41.4 32.7 14.3 13 18.9 49.9 31 13.5 6.8 14 11.4 45.5 24.8 16.6 5.8 15 28.9 55.4 18.2 19 9.8 16 28.6 57.3 14.6 22.8 11 17 41.9 63.5 37.9 34.2 13.5 18 49.2 71.1 23.1 13.6 11.5

Explanation / Answer

Using the data analysis add in in excel we get multiple linear regression:

1) parameters:

2) Y=-55.5+1.17*TV + .19*RADIO + .161*PRINT + .984*OTHER

3) Yes, overall model is significant since p-value:

4) a, b & c: significance of all the independent variables:

TV & RADIO are only significant at 95% confidence since their p-values are <0.05 whereas this is not the case for PRINT & OTHER.

5) Looking at R-sq value, we conclude that 96.77% of the variation in sales is explained by the amount of investments in TV, radio, print and other type of advertisements.

SUMMARY OUTPUT Regression Statistics Multiple R 0.983755 R Square 0.967773 Adjusted R Square 0.957858 Standard Error 2.678497 Observations 18 ANOVA df SS MS F Significance F Regression 4 2800.819 700.2046 97.59841 1.47E-09 Residual 13 93.26648 7.174345 Total 17 2894.085 Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0% Intercept -55.5036 5.488985 -10.1118 1.58E-07 -67.3618 -43.6454 -67.3618 -43.6454 tv 1.172678 0.183496 6.390758 2.38E-05 0.776259 1.569096 0.776259 1.569096 radio 0.192037 0.076034 2.525682 0.025331 0.027776 0.356298 0.027776 0.356298 print 0.161428 0.162483 0.993507 0.338596 -0.1896 0.512451 -0.1896 0.512451 other 0.984336 0.901884 1.091421 0.294903 -0.96407 2.932739 -0.96407 2.932739 RESIDUAL OUTPUT Observation Predicted sales Residuals 1 18.6298 -0.2298 2 25.53456 -3.73456 3 24.52317 -2.92317 4 32.01098 1.789017 5 17.55319 3.346807 6 15.21712 0.68288 7 51.53789 -2.03789 8 29.39018 -2.69018 9 28.64557 0.054425 10 21.70704 -2.00704 11 45.18048 0.619517 12 51.77806 2.621943 13 17.83893 1.061069 14 11.00461 0.395391 15 25.67144 3.228558 16 29.00283 -0.40283 17 45.04901 -3.14901 18 45.82513 3.374875

Related Questions

Navigate

• Browse (All)
• Browse C
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.