Question

$\bar{x} = 15.963$ $\bar{y} = 1.263$ $S_{XX} = 141.319$ $S_{YY} = 4.988$ $S_{XY} = 20.76$ $MSE = 0.0692$ $\sqrt{MSE \times [\frac{1}{n} + \frac{(x^* - \bar{x})^2}{S_{XX}}]}$ $\sqrt{MSE \times [1 + \frac{1}{n} + \frac{(x^* - \bar{x})^2}{S_{XX}}]}$ $\hat{y} = b_0 + b_1x$

Name: barx 15963 bary 1263 sxx 141319 syy 4988 sxy 2076 mse 00692 sqrtmse times frac1n fracx barx2sxx sqrtmse times 1 frac1n fracx barx2sxx haty b0 b1x 64365
Uploaded: 2022-11-08T18:22:26-08:00
Duration: 3 min 5 s
Channel: Sri K
Description: barx 15963 bary 1263 sxx 141319 syy 4988 sxy 2076 mse 00692 sqrtmse times frac1n fracx barx2sxx sqrtmse times 1 frac1n fracx barx2sxx haty b0 b1x 64365

          $\bar{x} = 15.963$
$\bar{y} = 1.263$
$S_{XX} = 141.319$
$S_{YY} = 4.988$
$S_{XY} = 20.76$
$MSE = 0.0692$
$\sqrt{MSE \times [\frac{1}{n} + \frac{(x^* - \bar{x})^2}{S_{XX}}]}$
$\sqrt{MSE \times [1 + \frac{1}{n} + \frac{(x^* - \bar{x})^2}{S_{XX}}]}$
$\hat{y} = b_0 + b_1x$

$barx 15963 bary 1263 sxx 141319 syy 4988 sxy 2076 mse 00692 sqrtmse times frac1n fracx barx2sxx sqrtmse times 1 frac1n fracx barx2sxx haty b0 b1x 64365$

Added by Joanna C.

Elementary Statistics a Step by Step Approach

Allan G. Bluman 9th Edition

Instant Answer

Solved by Expert Sri K

11/08/2022

Step 1

The least squares estimate of the slope is given by $b_1 = \frac{S_{XY}}{S_{XX}}$. $b_1 = \frac{20.76}{141.319} = 0.1469$ The least squares estimate of the intercept is given by $b_0 = \bar{y} - b_1\bar{x}$. $b_0 = 1.263 - 0.1469 \times 15.963 = 1.263 - 2.345 = Show more…

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$\bar{x} = 15.963$ $\bar{y} = 1.263$ $S_{XX} = 141.319$ $S_{YY} = 4.988$ $S_{XY} = 20.76$ $MSE = 0.0692$ $\sqrt{MSE \times [\frac{1}{n} + \frac{(x^* - \bar{x})^2}{S_{XX}}]}$ $\sqrt{MSE \times [1 + \frac{1}{n} + \frac{(x^* - \bar{x})^2}{S_{XX}}]}$ $\hat{y} = b_0 + b_1x$