Regression Model.

Regression Model.

Comment:

From the above plot, the law of demand holds. This is evident because when the price of goods or services rises, the quality demanded will fall. Consequently, when the quality of demand per certain period of time falls, this will definitely result in price rise and will rise as price falls, other things being equal (centra paribus) (Herbert, 2019).

On Equation on the plot,

Y=0.0521x+150.15

Y = is the dependent variable (Demand).

X₁= is the independent variable (Price).

0.0521 is the Coefficient of (x).

And 150.15 is the Intersection value.

• Demand for Coffee (Y), against Income of Coffee (x₂).

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Solution.

Comment:

From the above plot above, demand (Y) and Income (X₂) are inversely related. This clearly implies that increment in Income leads to Decrement in Demand (Y), and increment in Demand (Y) leads to Decrement in Income (X₂), other things being equal (centra paribus) (Herbert, 2019).

On Equation on the plot,

Y=0.1673x+34.105

Y = is the dependent variable (Demand).

X₂= is the independent variable (Income).

0.1673 is the Coefficient of (x).

And

34.105 is the Intersection value

2. Assuming the Demand for Coffee (Y) and price for coffee are linked by a linear relationship by using the ordinally Least square (OLS) method.

Solution.

Given that

= 4.516249

= 202.609051

3. Find Coefficients of determination, R², and comment on its value.

Solution.

R²=0.235138

From the results obtained and from the regression output, we can conclude that there is no significance in the difference between Demand and Price at 0.05 level of significance.

If you compare the R² in regression output and that of the scattered plot are equal.

4. Assuming the Demand for Coffee (Y) and price for coffee are linked by a linear relationship by using the ordinally Least square (OLS) method.

Given that

=

=

5. Find Coefficients of determination, R², and comment on its value.

Solution.

R²=0.931301

From the results obtained and from the regression output, we can conclude that there is no significance in the difference between Demand and Income at 0.05 level of significance.

If you compare the R² in regression output and that of the scattered plot are equal.

Section (B): Multivariate Regression Analysis.

6. Estimate the linear regression model for Demand (Y) and Price X₁ and Income X₂

Solution.

From the above findings, it’s very clear that we have a price coefficient, income coefficient, and also intercept of the dependent variable and the independent variables (Stockemer, 2019).

I.e.,

So

This is the estimated linear regression model in our case.

To obtain the gradients of each independent variable, we differentiate the regression model with respect to .

So for the price the gradient is  and for Income is

7. Compare the coefficients of Price for Coffee.

Solution.

   = 4.516249and = .

These being the two coefficients, they are different from one another. This is because there might be other predictor variables in the multivariate regression model.

8. State and discuss the Coefficient determination, R²

Solution.

In this case, we are going to look at R² for price and income on the bivariate regression model to that of multivariate.

For the price, the R² in Simple regression model is 0.235138 and for the multivariate regression model is 0.96832

For Income, the R² in Simple regression model is 0.931301and for the multivariate regression model is 0.96832

There is a difference between the two, and this implies that there is no significant relationship between the bivariate regression model and the multivariate regression model.

9. Comment on the validity of bivariate and multivariate analysis

 Solution.

 From the above analysis and findings, we can be able to see that Bivariate analysis only manages on testing the relationship between two paired data sets while the Multivariate majors on two or more variables, as we may say, and analyze the correlation among those variables.

However, they both tend to have a similar goal by the end of the day. The determine which variable influences or has an impact on the outcome or output.

10. Other factors that Influence Demand of coffee in the United Kingdom.

Solution.

1. Taste and Preference.

A positive change in tastes or preferences leads to an increment in demand.

An undesirable change in tastes and preferences will lead to a decrement in demand. If tastes and preferences sour (make demand decrement), then we would expect market price and market quantity to decrease (Winarno, 2018).

1. Population

As the population grows, there will be an increase in demand for goods and services. The more people are there, the more needs and wants are required to be satisfied. It’s not only the size of the population that affects demand, but the structure of the population also affects the demand (Winarno, 2018).

• Consumer Expectations

Consumer Expectations. If consumers expect a product’s price to fall, they will wait to buy the product when it is cheaper. In other words, demand falls. But if they expect the price to increase, they demand more of the product now, while it’s still cheap (Winarno, 2018).

1. Level of Income and Taxes

Primarily through their impact on demand. Tax cuts boost demand by increasing disposable income and by encouraging businesses to hire and invest more. Tax increases do the reverse. These demand effects can be substantial when the economy is weak but smaller when it is operating near capacity (Winarno, 2018).

Section (C): Co-efficient of variation.

11. Show which stock was riskier for each year.

Solution.

From the table given in the question paper, we are going to calculate the mean of means and mean of standard deviation;

Mean of means=

Mean of Standard Deviations=

Mean of means=

Mean of Standard Deviations=

Theoretically, Standard deviation helps determine market volatility or the spread of asset prices from their average cost. When prices move wildly, the standard deviation is high, meaning investors will be risky. Low standard deviation means prices are calm, so investments come with low risk (Sameera, 2016). Therefore having this Stock B was risker compared to Stock A.

            Reference

Tsakiris, M., Ainley, V., Pollatos, O., & Herbert, B. M. (2019). Comment on “Zamariola et al.,(2018), Interoceptive Accuracy Scores are Problematic: Evidence from Simple Bivariate Correlations”-The Empirical Data Base, the Conceptual Reasoning and the Analysis behind this Statement are Misconceived and do not Support the Authors’ Conclusions.

Stockemer, D. (2019). Multivariate Regression Analysis. In Quantitative Methods for the Social Sciences (pp. 163-174). Springer, Cham.

Winarno, S. T., & Harisudin, M. (2018). The Determinant Factor of Consumer Attitudes of the Robusta Coffee Processed in East Java, Indonesia. Journal of Entrepreneurship Education.

Sameera, S. K., Srinivas, T., Rajesh, A. P., Jayalakshmi, V., & Nirmala, P. J. (2016). Variability and path co-efficient for yield and yield components in rice. Bangladesh Journal of Agricultural Research, 41(2), 259-271.