Question

A financial planner tracks the number of new customers added each quarter for a 6 year...

A financial planner tracks the number of new customers added each quarter for a 6 year period. The data is presented below:

Year Quarter New Year Quarter New

2014 I 31 2017 I 69

II 24 II 54

III 23 III 46

IV 16 IV 32

2015 I 42 2018 I 82

II 35 II 66

III 30 III 51

IV 23 IV 38

2016 I 53 2019 I 91

II 45 II 72

III 39 III 59

IV 27 IV 41

Create a simple linear trend regression model. Let t=0 in 2013: IV. This is a computer deliverable.

(a) Interpret the slope coefficient.

(b) Test to see if the number of new customers is increasing over time. Use alpha = 0.01.

(c) Test to see if the model has explanatory power. Use alpha = 0.05.

(d) Forecast the number of new customers in the first and second quarters of 2020.

Create a multiple regression equation incorporating both a trend (t=0 in 2013: IV) and dummy variables for the quarters. Let the first quarter represent the reference (or base) group. Complete (e) thru (h) using your results. This is a computer deliverable.

(e) Test to see if there is an upward trend in new customers. Use alpha = 0.01.

(f) Test to see if the model has explanatory power. Use alpha = 0.05.

(g) Forecast the number of new customers in the first and second quarters of 2020.

(h) Test for the existence of first order autocorrelation, use alpha = 0.05. The calculated dw = 1.19.

Homework Answers

Answer #1

ANSWER:

We Used the given data and estimated a Simple linear regression equation

SUMMARY OUTPUT
Regression Statistics
Multiple R 0.652093
R Square 0.425225

Adjusted R

Square

0.399099

Standard

Error

15.31675
Observation 24
ANOVA
df SS MS F

Significance

F

Regression 1 3818.365 3818.365 16.27588 0.000555
Residual 22 5161.26 234.6027
Total 23 8979.625
Coefficients

Standard

Error

t Stat p-value Lower 95%

Upper

95%

Lower

95.0%

Upper

95.0%

Intercept 22.59783 6.453718 3.50152 0.002017 9.213633 35.98202 9.213633 35.98202
period 1.822174 0.451666 4.034338 0.000555 0.885476 2.758872 0.885476 2.758872

data used:

period New
1 31
2 24
3 23
4 16
5 42
6 35
7 30
8 23
9 53
10 45
11 39
12 27
13 69
14 54
15 46
16 32
17 82
18 66
19 51
20 38
21 91
22 72
23 59
24 41

(a) Every quarter ahead there is an expected increase of 1.82(approx 2) new customers.

(b) Yes,there is a significant increasing trend since slope for the time variables is positive and significant since p-value is 0.00056<0.001.

So reject H0 and conclude the variable(trend/time) is significant.

(c) Yes the model is significant since:

F

Significant

F

16.27588 0.000555

<0.05

So reject H0 and conclude regression is significant.

(d) Forecast:

2017-Q1 68.148
2017-Q2 69.97

Formula:

2017-Q1 =22.598+1.822*25
2017-Q2 =22.598+1.822*26
Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
For the data given below, forecast period 17 using following methods and suggest the best forecasting...
For the data given below, forecast period 17 using following methods and suggest the best forecasting model 1. Simple Moving Average (Three Period) 2. Weighted Average (50% on t-1, 30% on t-2, 20% on t-3) 3. Exponential Smoothing (α=.1), F1= y intercept from regression) 4. Exponential Smoothing (α=.3), F1= y intercept from regression) 5. Exponential Smoothing with trend (α=.3) and (δ=.3), F1= y intercept from regression)** 5. Exponential Smoothing with trend (α=.1) and (δ=.3), F1= y intercept from regression)** 6....
Consider the following time series data. Quarter Year 1 Year 2 Year 3 1 2 5...
Consider the following time series data. Quarter Year 1 Year 2 Year 3 1 2 5 7 2 0 2 6 3 5 8 10 4 5 8 10 (a) Choose the correct time series plot. (i) (ii) (iii) (iv) Plot (iii)- Select your answer -Plot (i)Plot (ii)Plot (iii)Plot (iv)Item 1 What type of pattern exists in the data? Positive trend pattern, no seasonality- Select your answer -Positive trend pattern, no seasonalityHorizontal pattern, no seasonalityNegative trend pattern, no seasonalityPositive trend...
Consider the following time series data. Quarter Year 1 Year 2 Year 3 1 2 4...
Consider the following time series data. Quarter Year 1 Year 2 Year 3 1 2 4 5 2 4 5 8 3 1 3 4 4 7 9 10 (a) Choose the correct time series plot. (i) (ii) (iii) (iv) - Select your answer -Plot (i)Plot (ii)Plot (iii)Plot (iv)Item 1 What type of pattern exists in the data? - Select your answer -Positive trend pattern, no seasonalityHorizontal pattern, no seasonalityNegative trend pattern, no seasonalityPositive trend pattern, with seasonalityHorizontal pattern, with...
Year Quarter Sales ($000) 2015 1 $400 2015 2 2,000 2015 3 3,500 2015 4 260...
Year Quarter Sales ($000) 2015 1 $400 2015 2 2,000 2015 3 3,500 2015 4 260 2016 1 740 2016 2 2,720 2016 3 4,900 2016 4 520 2017 1 1,500 2017 2 3,100 2017 3 6,520 2017 4 960 2018 1 1,840 2018 2 4,040 2018 3 7,680 2018 4 1,640 2019 1 3,520 2019 2 5,640 2019 3 8,900 2019 4 3,620 Problem 2 House Depot’s quarterly sales of a lawn, landscaping, and gardening items – like lawnmowers,...
1) What are some indicators that there are assignable causes for variation in a process? I.Process...
1) What are some indicators that there are assignable causes for variation in a process? I.Process capability. II. Data patters outside of the control limits. III. Data patters within the control limits. IV. Points randomly falling above and below the control chart center line. a. II and III b. II, III, IV c. I, II, IV d. I, II, III, IV 2) The best quantitative tool to determine the cause for variation in a process is: a. ANOVA b. Correllation...
f. Interpret the slope coefficient for one of the dummy variables included in your regression model....
f. Interpret the slope coefficient for one of the dummy variables included in your regression model. g. For the slope coefficient of the variable with the smallest slope coefficient (ignore sign, use absolute value), test to see if the “a priori” expectation from part (a) is confirmed. Use alpha = 0.05. h. Interpret the coefficient of determination in this situation. i. Test the explanatory power of the entire regression model. Please use alpha = 0.01. j. For the variable with...
Is there a relationship between the dollars spent each week on recreation and the number of...
Is there a relationship between the dollars spent each week on recreation and the number of members of the family? Do larger families spend more on recreation? Ten Chicago families shared the following information: Family Size               3         6        5        6        6        3        4         4         5        3 Amount Spent          99        104     151     129     142     111     74        91        119     91 a. What is the dependent variable (Y) in this situation? b. What is the independent variable (X) in this situation? c. Calculate...
For each scenario below, do the following: (1) Indicate which procedure you would use: (i) two-independent...
For each scenario below, do the following: (1) Indicate which procedure you would use: (i) two-independent sample t-test, (ii) paired t- test, (iii) chi-square goodness-of-fit test, (iv) chi-square test of independence, (v) t-test of a regression coefficient, (vi) an F −test for multiple regression, (vii) a one-way ANOVA, or (viii) a two-way ANOVA. (2) Based on your answer in (1), state the appropriate null and alternative hypotheses. (3) For all procedures except (i), state the degrees of freedom(s) for the...
“New drive-in movie theatres could be popping up by June” (Griffin, K., Vancouver Sun Newspaper, Thursday,...
“New drive-in movie theatres could be popping up by June” (Griffin, K., Vancouver Sun Newspaper, Thursday, May 14, 2020, p. A3). “Metro Vancouverites may soon be able to take their cars to watch movies at several new drive-in theatres. A group led by Howard Blank and ‘Point Blank Shows’ is looking at opening contemporary drive-ins around the region, including in Vancouver, Abbotsford, Langley, Burnaby, and West Vancouver. Blank said all local governments have responded favourably to the idea subject to...
Suppose that 44,000 people in New Zealand (population 4,400,000) carry a particular rare gene X that...
Suppose that 44,000 people in New Zealand (population 4,400,000) carry a particular rare gene X that places them at a higher risk of developing cancer. A medical test will correctly indicate the presence of gene X with 0.9 probability when carried out on a person who carries gene X. If the person does not carry gene X it will incorrectly indicate the presence of gene X with probability 0.05. (i) Draw a fully labelled tree diagram where the first branch...