Question

In: Statistics and Probability

Advertisement ($'000) Sales ($'000) 1068 4489 1026 5611 767 3290 885 4113 1156 4883 1146 &nbsp

Advertisement ($'000) Sales ($'000)

1068 4489

1026 5611

767 3290

885 4113

1156 4883

1146 5425

892 4414

938 5506

769 3346

677 3673

1184 6542

1009 5088

Construct a scatter plot with this data.
Do you observe a relationship between both variables?
Use Excel to fit a linear regression line to the data. What is the fitted regression model?
What is the slope? What does the slope tell us?Is the slope significant?
What is the intercept? Is it meaningful?
What is the value of the regression coefficient,r? What is the value of the coefficient of determination, r^2? What does r^2 tell us?
Use the model to predict sales and the business spends $950,000 in advertisement. Does the model underestimate or overestimates ales?

Expert Solution

Solution:

· Construct a scatter plot with this data.

The required scatter plot is given as below:

· Do you observe a relationship between both variables?

From above scatterplot we observe the positive linear relationship or association between the two variables.

· Use Excel to fit a linear regression line to the data. What is the fitted regression model?

The regression model by using Excel is given as below:

Regression Statistics
Multiple R	0.823733298
R Square	0.678536546
Adjusted R Square	0.6463902
Standard Error	592.7335727
Observations	12

ANOVA
	df	SS	MS	F	Significance F
Regression	1	7415845.784	7415845.784	21.10773517	0.00098869
Residual	10	3513330.883	351333.0883
Total	11	10929176.67

	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%
Intercept	-25.16823406	1042.259927	-0.024147752	0.981209823	-2347.468062	2297.131593
Advertisement	4.921595798	1.071235915	4.594315528	0.00098869	2.534733447	7.30845815

The regression equation is given as below:

Sales = -25.16823406 + 4.921595798*Advertisement

· What is the slope? What does the slope tell us?Is the slope significant?

The slope is given as b = 4.921595798. The slope tell us that there is an increment of 4.92 ($’000) in the sales as there is an increment of $1000 on advertisement.

The slope is statistically significant because corresponding p-value is given as 0.00098869 which is less than alpha value 0.05.

· What is the intercept? Is it meaningful?

The value of intercept is given as -25.16823406.

The intercept is not meaningful, because corresponding p-value is given as 0.9812 which is greater than alpha value 0.05.

· What is the value of the regression coefficient, r? What is the value of the coefficient of determination, r^2? What does r^2 tell us?

The value of the regression coefficient r is given as 0.823733298.

The value of the coefficient of determination is given as r^2 = 0.678536546.

This value indicated that about 67.85% of the variation in the dependent variable sale is explained by the independent variable advertisement.

· Use the model to predict sales and the business spends $950,000 in advertisement. Does the model underestimate or overestimates ales?

We have

Sales = -25.16823406 + 4.921595798*Advertisement

Advertisement = 950 thousand dollar ( or $950,000)

Sales = -25.16823406 + 4.921595798*950

Sales = 4650.347774

The value of sales is lies within range, so it is underestimate.

orchestra answered 1 year ago

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