Coefficient of Determination

PM – May 2021 – L2 – Q3 – Cost-Volume-Profit (CVP) Analysis

Forecast future sales using historical data and analyze which data period provides a better basis for forecasting.

Question

Some time ago, Robert launched a new product. Initially, sales were strong, but recent figures have raised concerns. Robert seeks a more accurate sales forecast to create detailed cash projections. The sales data below illustrates an underlying trend derived from an averaging method:

Year	Quarter	Trend Point (x)	Sales (Cartons) (y)
2016	3rd	1	10,000
2016	4th	2	10,760
2017	1st	3	10,920
2017	2nd	4	11,000
2017	3rd	5	11,050
2017	4th	6	11,080
2018	1st	7	11,085
2018	2nd	8	11,095
2018	3rd	9	11,120
2018	4th	10	11,130

On average, quarters 1 and 3 are 5% and 6% above the trend, respectively, while quarters 2 and 4 are 2% and 9% below it. Preliminary calculations for the 10 periods yield:

Linear Regression:
Slope: 82.67
Intercept: 10,472.33
Coefficient of determination: 0.535

Forecasting is needed for quarters 3 and 4 in 2019 and quarters 1 and 2 in 2020. There is a debate about using data from all 10 periods versus only the last 5. Analysis for the last five periods includes:

Results of last five periods‟ observations

(Note: y values are scaled down by 100 for ease of calculation.)

Required:
a. Forecast sales for the four quarters using the 10-period data. (8 Marks)
b. Prepare similar forecasts using the last five periods of data. (8 Marks)
c. Evaluate which data set provides the better forecast. (4 Marks)

Answer

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Tags: Coefficient of Determination, Linear Regression, Sales Forecasting, Seasonality, Trend Analysis
Level: Level 2

Topic: Cost-Volume-Profit (CVP) Analysis
Series: MAY 2021

QTB – Nov 2015 – L1 – SA – Q12 – Statistics

This question asks for the measure that explains how well the regression line fits the data.

Question

The measure that explains how well the regression line fits a set of data on daily sales of a product is known as coefficient of:

A. Rank Correlation
B. Product-Moment Correlation
C. Determination
D. Variation
E. Linear Regression

Answer

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Tags: Coefficient of Determination, Correlation, Regression Line
Level: Level 1

Topic: Statistics
Series: NOV 2015

QT – May 2017 – L1 – Q7 – Forecasting

Construct a scatter diagram and compute correlation, regression line, and coefficient of determination from given data.

Question

The following data gives how much 10 students of ICAG spend on TroTro to the Institute and food weekly:

Food (x)	10	12	14	16	18	20	22	24	26	28
TroTro (y)	25	24	22	20	19	17	13	12	11	10

Required:

a) Using a graph paper, construct a scatter diagram of the data.
(4 marks)

b) Determine the correlation coefficient.
(4 marks)

c) Calculate the coefficient of determination of the data and interpret its value.
(4 marks)

d) Determine the regression line of $y$ on $x$ , and interpret the coefficient.
(8 marks)

Answer

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Tags: Coefficient of Determination, Correlation Coefficient, Regression Line, Scatter Diagram
Level: Level 1

Topic: Forecasting
Series: MAY 2017

QT – May 2018 – L1 – Q7b – Forecasting

Calculate Pearson and Spearman correlation coefficients for production cost and output data.

Question

The secretariat of an association of industries gathered the following data from a random sample of member firms that produce similar products:

Required:
i) Compute the Pearson’s product moment correlation coefficient for the data. (6 marks)
ii) Hence, compute the coefficient of determination. (2 marks)
iii) Comment on your answer in (ii). (2 marks)
iv) Compute Spearman’s rank correlation coefficient for the data and comment on your answer. (8 marks)

Answer

Find Related Questions by Tags, levels, etc.

Tags: Coefficient of Determination, Correlation, Pearson Correlation, Ranking, Spearman Correlation
Level: Level 1

Topic: Forecasting
Series: MAY 2018

PM – May 2021 – L2 – Q3 – Cost-Volume-Profit (CVP) Analysis

Forecast future sales using historical data and analyze which data period provides a better basis for forecasting.

Question

Year	Quarter	Trend Point (x)	Sales (Cartons) (y)
2016	3rd	1	10,000
2016	4th	2	10,760
2017	1st	3	10,920
2017	2nd	4	11,000
2017	3rd	5	11,050
2017	4th	6	11,080
2018	1st	7	11,085
2018	2nd	8	11,095
2018	3rd	9	11,120
2018	4th	10	11,130

On average, quarters 1 and 3 are 5% and 6% above the trend, respectively, while quarters 2 and 4 are 2% and 9% below it. Preliminary calculations for the 10 periods yield:

Linear Regression:
Slope: 82.67
Intercept: 10,472.33
Coefficient of determination: 0.535

Results of last five periods‟ observations

(Note: y values are scaled down by 100 for ease of calculation.)

Answer

Find Related Questions by Tags, levels, etc.

Tags: Coefficient of Determination, Linear Regression, Sales Forecasting, Seasonality, Trend Analysis
Level: Level 2

Topic: Cost-Volume-Profit (CVP) Analysis
Series: MAY 2021

QTB – Nov 2015 – L1 – SA – Q12 – Statistics

This question asks for the measure that explains how well the regression line fits the data.

Question

The measure that explains how well the regression line fits a set of data on daily sales of a product is known as coefficient of:

A. Rank Correlation
B. Product-Moment Correlation
C. Determination
D. Variation
E. Linear Regression

Answer

Find Related Questions by Tags, levels, etc.

Tags: Coefficient of Determination, Correlation, Regression Line
Level: Level 1

Topic: Statistics
Series: NOV 2015

QT – May 2017 – L1 – Q7 – Forecasting

Construct a scatter diagram and compute correlation, regression line, and coefficient of determination from given data.

Question

The following data gives how much 10 students of ICAG spend on TroTro to the Institute and food weekly:

Food (x)	10	12	14	16	18	20	22	24	26	28
TroTro (y)	25	24	22	20	19	17	13	12	11	10

Required:

a) Using a graph paper, construct a scatter diagram of the data.
(4 marks)

b) Determine the correlation coefficient.
(4 marks)

c) Calculate the coefficient of determination of the data and interpret its value.
(4 marks)

d) Determine the regression line of $y$ on $x$ , and interpret the coefficient.
(8 marks)

Answer

Find Related Questions by Tags, levels, etc.

Tags: Coefficient of Determination, Correlation Coefficient, Regression Line, Scatter Diagram
Level: Level 1

Topic: Forecasting
Series: MAY 2017

QT – May 2018 – L1 – Q7b – Forecasting

Calculate Pearson and Spearman correlation coefficients for production cost and output data.

Question

The secretariat of an association of industries gathered the following data from a random sample of member firms that produce similar products:

Answer

Find Related Questions by Tags, levels, etc.

Tags: Coefficient of Determination, Correlation, Pearson Correlation, Ranking, Spearman Correlation
Level: Level 1

Topic: Forecasting
Series: MAY 2018

Question Tag: Coefficient of Determination

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PM – May 2021 – L2 – Q3 – Cost-Volume-Profit (CVP) Analysis

Forecast future sales using historical data and analyze which data period provides a better basis for forecasting.

QTB – Nov 2015 – L1 – SA – Q12 – Statistics

This question asks for the measure that explains how well the regression line fits the data.

QT – May 2017 – L1 – Q7 – Forecasting

Construct a scatter diagram and compute correlation, regression line, and coefficient of determination from given data.

QT – May 2018 – L1 – Q7b – Forecasting

Calculate Pearson and Spearman correlation coefficients for production cost and output data.

PM – May 2021 – L2 – Q3 – Cost-Volume-Profit (CVP) Analysis

Forecast future sales using historical data and analyze which data period provides a better basis for forecasting.

QTB – Nov 2015 – L1 – SA – Q12 – Statistics

This question asks for the measure that explains how well the regression line fits the data.

QT – May 2017 – L1 – Q7 – Forecasting

Construct a scatter diagram and compute correlation, regression line, and coefficient of determination from given data.

QT – May 2018 – L1 – Q7b – Forecasting

Calculate Pearson and Spearman correlation coefficients for production cost and output data.

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PM – May 2021 – L2 – Q3 – Cost-Volume-Profit (CVP) Analysis

Forecast future sales using historical data and analyze which data period provides a better basis for forecasting.

You're reporting an error for "PM – May 2021 – L2 – Q3 – Cost-Volume-Profit (CVP) Analysis"

QTB – Nov 2015 – L1 – SA – Q12 – Statistics

This question asks for the measure that explains how well the regression line fits the data.

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QT – May 2017 – L1 – Q7 – Forecasting

Construct a scatter diagram and compute correlation, regression line, and coefficient of determination from given data.

You're reporting an error for "QT – May 2017 – L1 – Q7 – Forecasting"

QT – May 2018 – L1 – Q7b – Forecasting

Calculate Pearson and Spearman correlation coefficients for production cost and output data.

You're reporting an error for "QT – May 2018 – L1 – Q7b – Forecasting"

PM – May 2021 – L2 – Q3 – Cost-Volume-Profit (CVP) Analysis

Forecast future sales using historical data and analyze which data period provides a better basis for forecasting.

You're reporting an error for "PM – May 2021 – L2 – Q3 – Cost-Volume-Profit (CVP) Analysis"

QTB – Nov 2015 – L1 – SA – Q12 – Statistics

This question asks for the measure that explains how well the regression line fits the data.

You're reporting an error for "QTB – Nov 2015 – L1 – SA – Q12 – Statistics"

QT – May 2017 – L1 – Q7 – Forecasting

Construct a scatter diagram and compute correlation, regression line, and coefficient of determination from given data.

You're reporting an error for "QT – May 2017 – L1 – Q7 – Forecasting"

QT – May 2018 – L1 – Q7b – Forecasting

Calculate Pearson and Spearman correlation coefficients for production cost and output data.

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