A theater technician charges a $200 flat fee and 5% of all profits from ticket sales per show. If the technician made $400 on a
2 answers:
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The line of best fit is a straight line that can be used to predict the
average daily attendance for a given admission cost.
Correct responses:
- The equation of best fit is;
- The correlation coefficient is; r ≈<u> -0.969</u>
The given data is presented in the following tabular format;
The equation of the line of best fit is given by the regression line
equation as follows;
Where;
= Predicted value of the<em> i</em>th observation
b₀ = Estimated regression equation intercept
b₁ = The estimate of the slope regression equation
= The <em>i</em>th observed value
= 24.625
= 960.625
Therefore;
Therefore;
- The slope given to the nearest tenth is b₁ ≈ -4.9
By using MS Excel, we have;
n = 8
∑X = 197
∑Y = 7365
∑X² = 4939
∑Y² = 6782675
∑X·Y = 180930
(∑X)² = 38809
Therefore;
- The y-intercept given to the nearest tenth is b₀ ≈ 1,042
The equation of the line of best fit is therefore;
The correlation coefficient is given by the formula;
Where;
Which gives;
The correlation coefficient given to the nearest thousandth is therefore;
- <u>Correlation coefficient, r ≈ -0.969</u>
Learn more about regression analysis here: