Respuesta :
From the given table, the year values, and prices, we have the following
equation and values;
(a) The least squares regression equation is; y ≈ 0.1316·x - 261.73
(b) The estimate of the price per gallon in 2030 is approximately $5.418
How can the equation and price be obtained from the table?
(a) The coefficients of the least squares regression formula are
presented as follows;
[tex]a = \mathbf{\overline y - b \cdot \overline x}[/tex]
[tex]b = \mathbf{\dfrac{\sum \left(x_i - \bar x\right) \times \left(y_i - \bar y\right) }{\sum \left(x_i - \bar x\right )^2 }}[/tex]
Entering the given values in MS Excel, we have;
[tex]\overline x[/tex] = 2005.1
[tex]\overline y[/tex] = 2.204
[tex]b = \dfrac{56.456 }{428.9} \approx 0.1316[/tex]
a = 2.204 - 0.1316 × 2005.1 ≈ -261.73
The least squares regression equation is therefore;
- [tex]\underline{y =0.1316\cdot x - 261.73}[/tex]
(b) In the year 2030, we have;
The price, y ≈ 0.1316 × 2030 - 261.73 = 5.418
In the year 2030, the price per gallon will be approximately $5.418
Learn more about least squares regression here:
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