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Question 3 (Answer all questions) Ramly MS, the owner of a musical instrument d...

May 7, 2024

Solution by Steps

step 1

To graph the data, plot the number of TV appearances on the x-axis and the demand for bass drums on the y-axis

step 2

Each pair of data points (TV appearances, bass drum demand) is plotted on the graph

step 3

After plotting all points, observe if they align or form a pattern that could suggest a linear relationship

a Answer

The graph is not provided here, but following these steps will help visualize the potential linear relationship.

Key Concept

Graphical representation of data

Explanation

Plotting data points on a graph helps to visually assess the relationship between two variables.

step 1

To use the least-squares regression method, calculate the means of both the x (TV appearances) and y (bass drum demand) data

step 2

Calculate the slope (m) of the regression line using the formula

m = \frac{\sum (x - \bar{x})(y - \bar{y})}{\sum (x - \bar{x})^2}

step 3

Calculate the y-intercept (b) of the regression line using the formula

b = \bar{y} - m\bar{x}

step 4

Combine the slope and y-intercept to form the regression equation

y = mx + b

b Answer

The specific regression equation is not provided here, but following these steps will yield the forecasting equation.

Key Concept

Least-squares regression method

Explanation

This method is used to find the line of best fit for a set of data by minimizing the sum of the squares of the vertical distances of the points from the line.

step 1

Use the regression equation derived from the least-squares method

step 2

Substitute the value of 9 for the number of TV appearances (x) into the regression equation to estimate bass drum sales (y)

c Answer

The estimated bass drum sales for 9 TV appearances is calculated using the regression equation.

Key Concept

Forecasting with regression

Explanation

The regression equation can be used to estimate the dependent variable (in this case, bass drum sales) for a given value of the independent variable (TV appearances).

step 1

To find the correlation coefficient (r), use the formula

r = \frac{n(\sum xy) - (\sum x)(\sum y)}{\sqrt{[n\sum x^2 - (\sum x)^2][n\sum y^2 - (\sum y)^2]}}

step 2

Calculate the coefficient of determination (

r^2

) by squaring the correlation coefficient

step 3

Interpret the correlation coefficient as the strength and direction of the linear relationship between the two variables

step 4

Interpret the coefficient of determination as the proportion of the variance in the dependent variable that is predictable from the independent variable

d Answer

The correlation coefficient (r) and the coefficient of determination (

r^2

) are calculated using the given formulas and data.

Key Concept

Correlation and determination coefficients

Explanation

The correlation coefficient measures the strength and direction of a linear relationship between two variables, while the coefficient of determination indicates how well the regression line represents the data.