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disa [49]
3 years ago
13

Mr. James McWhinney, president of Daniel-James Financial Services, believes there is a relationship between the number of client

contacts and the dollar amount of sales. To document this assertion, Mr. McWhinney gathered the following sample information. The X column indicates the number of client contacts last month and the Y column shows the value of sales ($ thousands) last month for each client sampled. Number of Contacts,x Sales ($ thousands),y14 24 23 30 12 14 48 90 20 28 50 85 16 30 55 120 46 80 50 110 Determine the regression equation.
Mathematics
1 answer:
vlada-n [284]3 years ago
5 0

Answer:

\sum_{i=1}^n x_i = 334

\sum_{i=1}^n y_i =611

\sum_{i=1}^n x^2_i =13970

\sum_{i=1}^n y^2_i =51581

\sum_{i=1}^n x_i y_i =26584

With these we can find the sums:

S_{xx}=\sum_{i=1}^n x^2_i -\frac{(\sum_{i=1}^n x_i)^2}{n}=13970-\frac{334^2}{10}=2814.4

S_{xy}=\sum_{i=1}^n x_i y_i -\frac{(\sum_{i=1}^n x_i)(\sum_{i=1}^n y_i)}{n}=26584-\frac{334*611}{10}=6176.6

And the slope would be:

m=\frac{6176.6}{2814.4}=2.195

Nowe we can find the means for x and y like this:

\bar x= \frac{\sum x_i}{n}=\frac{334}{10}=33.4

\bar y= \frac{\sum y_i}{n}=\frac{611}{10}=61.1

And we can find the intercept using this:

b=\bar y -m \bar x=61.1-(2.195*33.4)=-12.213

So the line would be given by:

y=2.195 x -12.213

Step-by-step explanation:

The data given on this case is:

x: 14,12,20,16,46,23,48,50,55,50

y: 24,24,28,30,80,30,90,85,120,110

For this case we need to calculate the slope with the following formula:

m=\frac{S_{xy}}{S_{xx}}

Where:

S_{xy}=\sum_{i=1}^n x_i y_i -\frac{(\sum_{i=1}^n x_i)(\sum_{i=1}^n y_i)}{n}

S_{xx}=\sum_{i=1}^n x^2_i -\frac{(\sum_{i=1}^n x_i)^2}{n}

So we can find the sums like this:

\sum_{i=1}^n x_i = 334

\sum_{i=1}^n y_i =611

\sum_{i=1}^n x^2_i =13970

\sum_{i=1}^n y^2_i =51581

\sum_{i=1}^n x_i y_i =26584

With these we can find the sums:

S_{xx}=\sum_{i=1}^n x^2_i -\frac{(\sum_{i=1}^n x_i)^2}{n}=13970-\frac{334^2}{10}=2814.4

S_{xy}=\sum_{i=1}^n x_i y_i -\frac{(\sum_{i=1}^n x_i)(\sum_{i=1}^n y_i)}{n}=26584-\frac{334*611}{10}=6176.6

And the slope would be:

m=\frac{6176.6}{2814.4}=2.195

Nowe we can find the means for x and y like this:

\bar x= \frac{\sum x_i}{n}=\frac{334}{10}=33.4

\bar y= \frac{\sum y_i}{n}=\frac{611}{10}=61.1

And we can find the intercept using this:

b=\bar y -m \bar x=61.1-(2.195*33.4)=-12.213

So the line would be given by:

y=2.195 x -12.213

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