least squares regression

QMDM – JULY 2020 – L2 – Q2 – Regression Analysis on Training Allowances

Derive the regression equation for staff allowances based on training days, interpret parameters, predict for 11 days, and discuss suitability for 2-month prediction.

Question

The Human Resource Manager of a bank was worried about the number of international training programmes attended by the staff every year(x) and the corresponding allowances (GHe y). A random sample of 10 training programmes gave the following results:

x (days)	10	3	8	17	5	9	14	16	21	13
Staff Allowance(y) (GHe)	116	39	85	159	61	94	143	178	225	134

(a) Find an equation of the regression line of Y on X in the form Y = a + bX. (10 marks)

(b) Interpret the slope b and intercept a of your line. (5 marks)

(c) Find the expected allowance to be paid for a training programme that lasted for 11 days. (5 marks)

(d) State and give a reason, whether or not you would use the line to find the expected training lasting for 2 months. (5 marks)

Answer

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Tags: Extrapolation Limitations, least squares regression, prediction, Slope and Intercept Interpretation
Level: Level 2

QMDM – OCT 2022 – L2 – Q5 – Bivariate Data and Regression Analysis

Analyze bivariate data on median household income and percentage of mortgage-paying homeowners spending over 30% on housing costs in eight Ghanaian regions, explain bivariate data, draw scatter diagram and line, comment on relationship, calculate least squares line, and compare lines.

Question

Nationwide, about 27% of mortgage-paying home owners spent 30% or more of their income on
housing costs. Upper East region residents paid the largest percentage at 41% and the Greater
Accra residents the smallest at 17.5%. Eight regions were randomly selected, and the median
household income(X) in thousands and percentage of mortgage -paying homeowners whose housing
costs exceed 30 % of their income (Y) are as follows:

Regions Greater
Accra

Upper East

Bono
East

Ashanti Volta
Eastern Western Savannah

X 46.5 51.1 37.1 36.4 33.5 35.2 45.6 28.6 Y 37.2 41.0 20.6 24.3 22.0 17.5 30.0 23.0

(a) Briefly explain the term (X,Y) is bivariate data (b) Draw

(i) Scatter diagram for the data above (ii) a line through the points (c) Using (b) comment on the relationship between X and Y. (d) Calculate the least square line (e) Comment on the lines in (b)-(ii) and (d) above.

Answer

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Tags: Bivariate Data, Correlation, data presentation, hypothesis testing, least squares regression, Scatter Diagram
Level: Level 2

QMDM – APR 2023 – L2 – Q3 – Regression Analysis for Mistakes and Checks

Analyze mistakes vs. checks data with scatter plot, regression, determination coefficient, and prediction.

Question

Yaa Tabua Travel arrange a large number of holidays, and in some of these they make administrative mistakes. They are about to change their quality control procedures, and have done some experiments to see how the number of mistakes varies with the number of checks. The following table shows their findings:

Checks	0	1	2	3	4	5	6	7	8	9	10
Mistakes	92	86	81	72	67	59	53	43	32	24	12
(a) Draw a scatter plot of the data; identify the independent variable, x, and the dependent variable, y. [5 Marks]
(b) Determine the least square estimates of the regression constant, a, and the regression coefficient, b. i.e y=a+bx. [4 Marks]
(c) Comment on your estimates in (b) above. [2 Marks]
(d) Calculate the coefficient of determination. [6 Marks]
(e) Using your line in (b), predict how many mistakes Yaa Tabua would expect with 20 checks and comment on its reliability. [4 Marks]
(f) Use your estimate in (d), to comment on the suitability of your estimate in (e) above. [4 Marks]

Answer

Find Related Questions by Tags, levels, etc.

Tags: Coefficient of Determination, least squares regression, prediction, Reliability, Scatter Plot
Level: Level 2

QMDM – JULY 2020 – L2 – Q2 – Regression Analysis on Training Allowances

Derive the regression equation for staff allowances based on training days, interpret parameters, predict for 11 days, and discuss suitability for 2-month prediction.

Question

x (days)	10	3	8	17	5	9	14	16	21	13
Staff Allowance(y) (GHe)	116	39	85	159	61	94	143	178	225	134

(a) Find an equation of the regression line of Y on X in the form Y = a + bX. (10 marks)

(b) Interpret the slope b and intercept a of your line. (5 marks)

(c) Find the expected allowance to be paid for a training programme that lasted for 11 days. (5 marks)

(d) State and give a reason, whether or not you would use the line to find the expected training lasting for 2 months. (5 marks)

Answer

Find Related Questions by Tags, levels, etc.

Tags: Extrapolation Limitations, least squares regression, prediction, Slope and Intercept Interpretation
Level: Level 2

QMDM – OCT 2022 – L2 – Q5 – Bivariate Data and Regression Analysis

Analyze bivariate data on median household income and percentage of mortgage-paying homeowners spending over 30% on housing costs in eight Ghanaian regions, explain bivariate data, draw scatter diagram and line, comment on relationship, calculate least squares line, and compare lines.

Question

Regions Greater
Accra

Upper East

Bono
East

Ashanti Volta
Eastern Western Savannah

X 46.5 51.1 37.1 36.4 33.5 35.2 45.6 28.6 Y 37.2 41.0 20.6 24.3 22.0 17.5 30.0 23.0

(a) Briefly explain the term (X,Y) is bivariate data (b) Draw

Answer

Find Related Questions by Tags, levels, etc.

Tags: Bivariate Data, Correlation, data presentation, hypothesis testing, least squares regression, Scatter Diagram
Level: Level 2

QMDM – APR 2023 – L2 – Q3 – Regression Analysis for Mistakes and Checks

Analyze mistakes vs. checks data with scatter plot, regression, determination coefficient, and prediction.

Question

Checks	0	1	2	3	4	5	6	7	8	9	10
Mistakes	92	86	81	72	67	59	53	43	32	24	12
(a) Draw a scatter plot of the data; identify the independent variable, x, and the dependent variable, y. [5 Marks]
(b) Determine the least square estimates of the regression constant, a, and the regression coefficient, b. i.e y=a+bx. [4 Marks]
(c) Comment on your estimates in (b) above. [2 Marks]
(d) Calculate the coefficient of determination. [6 Marks]
(e) Using your line in (b), predict how many mistakes Yaa Tabua would expect with 20 checks and comment on its reliability. [4 Marks]
(f) Use your estimate in (d), to comment on the suitability of your estimate in (e) above. [4 Marks]

Answer

Find Related Questions by Tags, levels, etc.

Tags: Coefficient of Determination, least squares regression, prediction, Reliability, Scatter Plot
Level: Level 2

Question Tag: least squares regression

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QMDM – JULY 2020 – L2 – Q2 – Regression Analysis on Training Allowances

Derive the regression equation for staff allowances based on training days, interpret parameters, predict for 11 days, and discuss suitability for 2-month prediction.

QMDM – OCT 2022 – L2 – Q5 – Bivariate Data and Regression Analysis

Analyze bivariate data on median household income and percentage of mortgage-paying homeowners spending over 30% on housing costs in eight Ghanaian regions, explain bivariate data, draw scatter diagram and line, comment on relationship, calculate least squares line, and compare lines.

QMDM – APR 2023 – L2 – Q3 – Regression Analysis for Mistakes and Checks

Analyze mistakes vs. checks data with scatter plot, regression, determination coefficient, and prediction.

QMDM – JULY 2020 – L2 – Q2 – Regression Analysis on Training Allowances

Derive the regression equation for staff allowances based on training days, interpret parameters, predict for 11 days, and discuss suitability for 2-month prediction.

QMDM – OCT 2022 – L2 – Q5 – Bivariate Data and Regression Analysis

Analyze bivariate data on median household income and percentage of mortgage-paying homeowners spending over 30% on housing costs in eight Ghanaian regions, explain bivariate data, draw scatter diagram and line, comment on relationship, calculate least squares line, and compare lines.

QMDM – APR 2023 – L2 – Q3 – Regression Analysis for Mistakes and Checks

Analyze mistakes vs. checks data with scatter plot, regression, determination coefficient, and prediction.

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QMDM – JULY 2020 – L2 – Q2 – Regression Analysis on Training Allowances

Derive the regression equation for staff allowances based on training days, interpret parameters, predict for 11 days, and discuss suitability for 2-month prediction.

You're reporting an error for "QMDM – JULY 2020 – L2 – Q2 – Regression Analysis on Training Allowances"

QMDM – OCT 2022 – L2 – Q5 – Bivariate Data and Regression Analysis

Analyze bivariate data on median household income and percentage of mortgage-paying homeowners spending over 30% on housing costs in eight Ghanaian regions, explain bivariate data, draw scatter diagram and line, comment on relationship, calculate least squares line, and compare lines.

You're reporting an error for "QMDM – OCT 2022 – L2 – Q5 – Bivariate Data and Regression Analysis"

QMDM – APR 2023 – L2 – Q3 – Regression Analysis for Mistakes and Checks

Analyze mistakes vs. checks data with scatter plot, regression, determination coefficient, and prediction.

You're reporting an error for "QMDM – APR 2023 – L2 – Q3 – Regression Analysis for Mistakes and Checks"

QMDM – JULY 2020 – L2 – Q2 – Regression Analysis on Training Allowances

Derive the regression equation for staff allowances based on training days, interpret parameters, predict for 11 days, and discuss suitability for 2-month prediction.

You're reporting an error for "QMDM – JULY 2020 – L2 – Q2 – Regression Analysis on Training Allowances"

QMDM – OCT 2022 – L2 – Q5 – Bivariate Data and Regression Analysis

Analyze bivariate data on median household income and percentage of mortgage-paying homeowners spending over 30% on housing costs in eight Ghanaian regions, explain bivariate data, draw scatter diagram and line, comment on relationship, calculate least squares line, and compare lines.

You're reporting an error for "QMDM – OCT 2022 – L2 – Q5 – Bivariate Data and Regression Analysis"

QMDM – APR 2023 – L2 – Q3 – Regression Analysis for Mistakes and Checks

Analyze mistakes vs. checks data with scatter plot, regression, determination coefficient, and prediction.

You're reporting an error for "QMDM – APR 2023 – L2 – Q3 – Regression Analysis for Mistakes and Checks"

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