How to Analyze the Regression Analysis Output from Excel
In a simple regression model, we determine if variable Y is linearly dependent on variable X, meaning that whenever X changes, Y also changes linearly. A linear relationship is a straight line relationship, expressed as Y = α + βX + e. Here, Y is the dependent variable, and X is the independent variable. α is the intercept of the regression line, and β is the slope of the regression line. e is the random disturbance term.
The equation Y = α + βX (ignoring the disturbance term “e”) gives the average relationship between the values of Y and X. For example, if Y is the cost of goods sold and X is the sales, and α = 2 and β = 0.75, and if the sales are 100, i.e., X = 100, the cost of goods sold would be, on average, 2 + 0.75(100) = 77. However, in any particular year when sales X = 100, the actual cost of goods sold can deviate randomly around 77. This deviation from the average is called the “disturbance” or the “error” and is represented by “e”.
Also, in the equation Y = 2 + 0.75X + e, i.e., Cost of goods sold = 2 + 0.75 (sales) + e, the interpretation is that the cost of goods sold increases by 0.75 times the increase in sales. For example, if the sales increase by 20, the cost of goods sold increases, on average, by 0.75 (20) = 15. In general, we are much more interested in the value of the slope of the regression line, β, than in the value of the intercept, α.
Suppose we are trying to determine if there is a relationship between two variables that apparently have no relationship, say the sales of a firm and the average height of employees of the firm. We would set up an equation like the following: Y = α + βX + e, where Y = sales of the firm, X = average height of employees, α = intercept of the regression line, β = slope of the regression line, and e = disturbance term. Then, we would collect a sample of data from a number of firms regarding sales and average height of employees.
They will want to know both employment rates as well as types of employment. They should look at marital status, median age, and household size. Customer lifestyles and preferences are another important aspect of gathering demographic information. Hobbies and activities popular among customers in this area should be examined. Do they enjoy active, outdoor activities, or do they typically prefer indoor activities such as going to the movies and shopping at malls?
Andy also needs to analyze how this data has impacted his company. To do so, Andy needs input from his quality and sales departments so he calls a meeting where he shares his data. Andy learns that a recent sales order was cancelled over no product being in stock, and that the quality issues have forced detailed inspections of each item delivered by AWI, which has led to a high amount of overtime. Andy asks these department managers to use the “Cause and Effect” method to determine the dollar value of loss from these issues. This will allow Andy to see how each cause (delivery and quality) lead to a monetary impact to
Regression analysis is also used to understand which among the independent variables are related to the dependent variable, and to explore the forms of these relationships. In restricted circumstances, regression analysis can be used to infer causal relationships between the independent and dependent variables. However this can lead to illusions or false relationships, so caution is advisable;[2] for example, correlation does not imply
In the example above, the survey needed not only to be expanded but diversified. By including the women and other workers, you make the statistics more accurate because it represents the TV watching habits of ALL the company’s employees. However, if the company is very large, it would be difficult to interview every single employee. The solution to this problem is called random representative sampling.
The sales director proposed that if the firm were to reduce the price of Item 345 to FF15.00/m, they would be able to increase sales to 175,000 units (or 25% of industry volume). But if they were to keep the price at the current value of FF20.00/m, they would be able to sell not less than 75,000 units (or 11% of industry volume).
Our predicted points for our data are, (13, -88.57) and (-2, -29.84). These points show the
F = x/y = lFl x ((δx/IxI) + (δy/lyl)) was used for the error propagation of 1/d where x = 1 and y = d. This equation was also used for the error propagation of κ = slope/ ε0A where x = slope and y = A.
An investigation of 150 randomly selected local restaurants concluded that 42% of local restaurants have serious health code violations. Is this a population or a sample; explain your answer.
Now we can use techniques from linear regression to solve the problem. After the transformation, the least squares method will be used to predict those unknown betas. The core concept of the least squares method is to make the sum of (y-ye)2 the least (Jia, 2011). There is no need to calculate them by ourselves because the process is complex. We usually use computer to assist us to get the results of the least squares method.
Sales growing at a faster rate than cost of goods sold. Projected FY4 and FY5 also had projected sales growing faster than cost of goods sold. See graph for details (Derived from Exhibit 1).
A fraction-of-a-cent cost change can represent a large dollar change in overall profitability, when selling millions of units of product a month. Managers must carefully watch per unit costs on a daily basis through the production process, while at the same time dealing with materials and output in huge quantities” (From Academic
A change in quantity supplied is just a movement from one point to another in the supply curve. In opposite, the cause of a change in supply is a change in one the determinants of supply that shifts the curve either to the left or the right. These determinants are the resource prices, technology, taxes and subsidies, producer expectations, and number of sellers. An equilibrium price is required to produce an equilibrium quantity and a price below that amount is referred as quantity supplied of zero no firms that are entering that particular business. If the coefficient of price is greater than zero, as the price of the output goes up, firms wants to produce more of that output. As the price of the output goes up it becomes more appealing for the firms to shift resources into the production of that output. Therefore, the slope of a supply curve is the change in price divided by the change in quantity. The constant in this equation is something less (negative number always) than zero because it requires strictly a positive...
When two or more variables move in sympathy with the other, then they are said to be correlated. If both variables move in the same direction, then they are said to be positively correlated. If the variables move in opposite direction, then they are said to be negatively correlated. If they move haphazardly, then there is no correlation between them. Correlation analysis deals with the following:
Often uses random sampling to select a large statistically representative sample from which generalizations can be drawn.
Thirdly, linear regression assumes that there is little or no multicollinearity in the data. Multicollinearity occurs when the independent variables are too highly correlated with each other.