Managerial Statistics Chapter 7 Quiz

The least square method utilizes the normal equations $ΣΥ = n a + b ΣΧ$ and $ΣΧΥ = a ∑X + b ΣΧ²$ to estimate 'a' and 'b', where 'n' is the number of data points and $ΣX$ is adjusted to 0 for simplification.

The constant 'a' represents the mean of Y and is calculated using the formula $a = \frac{ΣY}{n}$, where 'n' is the number of data points.

Using the formula $b = \frac{ΣXY}{ΣX²} = \frac{50}{25} = 2$.

<p>Obtaining two points on graph paper allows us to create a straight line that represents the trend, serving as a visual aid to better understand the data relationship.</p> Signup and view all the answers

<p>The moving average method calculates the average of a dataset over specific intervals, smoothing out fluctuations to reveal the underlying trend in the data.</p> Signup and view all the answers

<p>A time series is a collection of values of a variable recorded at different time periods.</p> Signup and view all the answers

<p>Secular trend and seasonal variation.</p> Signup and view all the answers

<p>It aids in profit planning and sales forecasting, among other applications.</p> Signup and view all the answers

<p>Secular trend refers to the long-term movement or direction of a time series.</p> Signup and view all the answers

<p>Seasonal variation.</p> Signup and view all the answers

<p>They can be used for data management and performing calculations to analyze time series data.</p> Signup and view all the answers

<p>Processes like sales trends, stock market changes, and economic forecasting can be analyzed.</p> Signup and view all the answers

<p>Cyclical variation occurs over longer, irregular intervals, while seasonal variation follows a fixed, predictable pattern.</p> Signup and view all the answers

<p>Factors include increase in population, technological progress, and changes in consumer demands.</p> Signup and view all the answers

<p>Seasonal variations occur regularly within a year, while cyclical variations have longer, irregular durations and do not follow a predictable pattern.</p> Signup and view all the answers

<p>Examples include increased sales of woolen clothes in winter and higher ice cream sales in summer.</p> Signup and view all the answers

<p>The four phases are depression, boom, recovery, and decline.</p> Signup and view all the answers

<p>Irregular variations are erratic fluctuations due to unforeseen factors such as floods or wars.</p> Signup and view all the answers

<p>The moving average method smooths out short-term fluctuations to identify longer-term trends in data.</p> Signup and view all the answers

<p>In this method, data points are plotted on a graph with 'Time' on the X-axis and 'Data' on the Y-axis, and a smooth curve is drawn to represent the trend.</p> Signup and view all the answers

<p>The data is divided into two equal parts; averages are calculated for each part and plotted against the mid-point of each half.</p> Signup and view all the answers