The management of the VitalPro Inc. compared daily observations of sales revenue and number of ad clicks from the online marketing campaigns. They think that more Ad Clicks translates into more Sales, and they have a strong feeling that VitalPro Inc. can increase the revenue by improving CTR (click-through rate).

A group of Humber College students from e-Business Marketing program has been entrusted with the regression analysis. A random sample of 30 daily recordings is shown below. (Sales are in$ thousands.)

ay#	AdClicks	Sales
1	433	677
2	470	591
3	595	660
4	549	579
5	569	536
6	662	772
7	652	660
8	621	780
9	705	823
10	785	924
11	550	845
12	404	438
13	616	656
14	414	482
15	531	850
16	453	439
17	607	997
18	666	750
19	416	531
20	674	894
21	444	602
22	461	724
23	824	901
24	785	943
25	518	582
26	464	436
27	556	664
28	380	452
29	603	955
30	542	592

Humber students urgently prepared a regression analysis report. Unfortunately, it was the final exam week, and students had very little time. At that moment, only first 10 daily observations were available. Also, the students had no time to find the regression equation,rr, andR2R2. The following picture is the draft that they prepared.

1234567891011

(a) Check the draft. Select the most appropriate comment.

• The roles of the selected variables are mixed up. AdClicks should be the independent variablexx, and Sales should be considered as the dependent variableyy, not the other way around.
• The draft looks incomplete as the students forgot to label the axes. Also, I would probably make the points (Excel markers) bigger.
• The choice of dependent and independent variables is wrong. The students must have taken AdClicks (not Day#) as the independent variablexx, and Sales should be the dependent variableyy.
• The choice of dependent and independent variables is correct, but the trend line is missing.
• None of the above.

Please help the Humber College students. Using Excel and 30 daily recordings, please construct a scatter diagram to support or reject the idea of the management. Make sure that you do not repeat the possible mistakes that are described in question 1. Also, please include the regression equation andR2R2in the scatter diagram along with the trend line. Based on the result, answer the following questions:

b)Round your answers to 4 decimal places.

The coefficient of determination is R2=R2=

The linear correlation coefficient is r=r=

(c)Round your answers to 2 decimal places.

The regression equation is(do not mix upb0b0andb1b1)

y=y^= ++ xx

(d)Express your answers in percent form (i.e. 3.00% instead of 0.03) and round to 2 decimal places.

What percent of the variation in Sales can be explained by the variation in AdClicks? %

What percent of the variation in Sales cannot be explained by the variation in AdClicks, but is due to other factors? %

(e)Round your answers to 2 decimal places.

What is the slope of the regression equation?

(f) How much will the sales revenue amount be expected to change if the number of daily ad clicks increases by one click?Please note that the answer is expected in dollars, not in thousands.

Select an answer decreases by the clicks of decreases by $ It does not change. I put zero to the next cell. increases by the clicks of increases by $

(g) What would be the best predicted sales revenue amount if the number of daily ad clicks is 736?Please note that the answer is expected in dollars, not in thousands.

$

(h) Would it be possible to use this regression model to predict the sales revenue amount if the number of daily ad clicks is 905 ?

• The forecast would be reliable. Just plug the given number of clicks into the regression equation.
• The forecast would be reliable, as the regression equation from question (c) can be used to predict any Sales.
• The forecast would be reliable, and Sales is approximately 1064.62.
• The forecast would not be reliable, as 905 clicks is not within the samplexx-range.
• None of the above.

(i) Does there appear to be a significant linear relationship between the sales revenue (Sales) and number of ad clicks (AdClicks) in the population of all daily observations at 4% significance level?

The following values are available in the Excel output.

RoundPP-value to 8 decimal places or use scientific notation.

PP-value==

Roundtsttst andFstFst values to 3 decimal places.

tst=tst=

FstFst=

What is your conclusion?

• At the 4% significance level, the sample data support the claim that there is the linear relationship between the sales revenue (Sales) and number of ad clicks (AdClicks) in the population of all daily observations.
• At the 4% significance level, there is not sufficient sample evidence to support the claim that that there is the linear relationship between the sales revenue (Sales) and number of ad clicks (AdClicks) in the population of all daily observations.
• None of the above.

Do not forget to attach the original Excel file(s).

Add Work

b)Round your answers to 4 decimal places.

The coefficient of determination is R2=R2=

The linear correlation coefficient is r=r=

(c)Round your answers to 2 decimal places.

The regression equation is(do not mix upb0b0andb1b1)

y=y^= ++ xx

(d)Express your answers in percent form (i.e. 3.00% instead of 0.03) and round to 2 decimal places.

What percent of the variation in Sales can be explained by the variation in AdClicks? %

What percent of the variation in Sales cannot be explained by the variation in AdClicks, but is due to other factors? %

(e)Round your answers to 2 decimal places.

What is the slope of the regression equation?

(f) How much will the sales revenue amount be expected to change if the number of daily ad clicks increases by one click?Please note that the answer is expected in dollars, not in thousands.

Select an answer decreases by the clicks of decreases by $ It does not change. I put zero to the next cell. increases by the clicks of increases by $

(g) What would be the best predicted sales revenue amount if the number of daily ad clicks is 736?Please note that the answer is expected in dollars, not in thousands.

$

(h) Would it be possible to use this regression model to predict the sales revenue amount if the number of daily ad clicks is 905 ?

• The forecast would be reliable. Just plug the given number of clicks into the regression equation.
• The forecast would be reliable, as the regression equation from question (c) can be used to predict any Sales.
• The forecast would be reliable, and Sales is approximately 1064.62.
• The forecast would not be reliable, as 905 clicks is not within the samplexx-range.
• None of the above.

(i) Does there appear to be a significant linear relationship between the sales revenue (Sales) and number of ad clicks (AdClicks) in the population of all daily observations at 4% significance level?

The following values are available in the Excel output.

RoundPP-value to 8 decimal places or use scientific notation.

PP-value==

Roundtsttst andFstFst values to 3 decimal places.

tst=tst=

FstFst=

What is your conclusion?

• At the 4% significance level, the sample data support the claim that there is the linear relationship between the sales revenue (Sales) and number of ad clicks (AdClicks) in the population of all daily observations.
• At the 4% significance level, there is not sufficient sample evidence to support the claim that that there is the linear relationship between the sales revenue (Sales) and number of ad clicks (AdClicks) in the population of all daily observations.
• None of the above.

Do not forget to attach the original Excel file(s).

Add Work