Question

Question 6 of 11 Step 1 of 6 No Time Limit The table below gives the list price and the number of bids received for five randomly selected items sold through online auctions. Using this data, consider the equation of the regression line, û = bo + bjx, for predicting the number of bids an item will receive based on the list price. Keep in mind, the correlation coefficient may or may not be statistically significant for the data given. Remember, in practice, it would not be appropriate to use the regression line to make a prediction if the correlation coefficient is not statistically significant.
Price in Dollars 23 34 44 46 50
Number of Bids 1 2 4 9 10
Step 1 of 6: Find the estimated slope. Round your answer to three decimal places.​

Answer 1

The estimated slope is approximately 2.344

The given table is presented as follows;

$\begin{array}{ccc}Number \ of Bids &&Price \ in \ Dollars\\1&&23\\2&&34\\4&&44\\9&&46\\10&&50\end{array}$

The regression line formula to be considered = $\bar u = b_0 + b\cdot \bar x$

The required parameter is;

The estimated slope

The method to find the estimate slope;

The least squares regression formula (method) is presented as follows;

$\bar u = b_0 + b\cdot \bar x$

Where;

b₀ = The y-intercept

$\mathbf{ b = \dfrac{\sum \left(x_i - \bar x\right) \times \left(u_i - \bar u\right) }{\sum \left(x_i - \bar x\right )^2 } = The \ estimated \ slope}$

From MS Excel, we have;

$\bar x$ = 5.2, $\bar u$ = 39.4

$\sum \left(x_i - \bar x\right) \times \left(u_i - \bar u\right)$ = 156.6

${\sum \left(x_i - \bar x\right )^2 }$ = 66.8

Therefore;

The estimated slope, b = 156.6/66.8 ≈ 2.344 (by rounding the answer to three decimal places)

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