Sam Johnston
2022-03-17

You can still ask an expert for help

asked 2022-03-28

asked 2022-04-04

A 6.0 cm diameter horizontal pipe gradually narrows to 2.0 centimeters. When water flows through this pipe at a certain rate, the gauge pressure in these two sections is 32.0 kPa and 24.0 kPa, respectively. What is the volume rate of flow ?

asked 2022-04-01

A penny of mass 3.1 g rests on a small 29.1 g block supported by a spinning disk of radius 8.3 cm. The coefficients of friction between block and disk are 0.742 (static) and 0.64 (kinetic) while those for the penny and block are 0.617 (static) and 0.45 (kinetic).

asked 2022-04-10

*to *4x^2y"+17y=0, y(1)=-1, y'(1)= -1/2

asked 2022-04-25

Simple Linear Regression - Difference between predicting and estimating?

Here is what my notes say about estimation and prediction:

Estimating the conditional mean

"We need to estimate the conditional mean $\beta}_{0}+{\beta}_{1}{x}_{0$ at a value $x}_{0$, so we use $\hat{{Y}_{0}}=\hat{{\beta}_{0}}+\hat{{\beta}_{1}}{x}_{0}$ as a natural estimator." here we get

$\hat{{Y}_{0}}~N({\beta}_{0}+{\beta}_{1}{x}_{0},{\sigma}^{2}{h}_{00})\text{}\text{where}{h}_{00}=\frac{1}{n}+\frac{{({x}_{0}-\stackrel{\u2015}{x})}^{2}}{(n-1){s}_{x}^{2}}$

with a confidence interval for $E\left({Y}_{0}\right)={\beta}_{0}+{\beta}_{1}{x}_{0}$ is

$(\hat{{b}_{0}}+\hat{{b}_{1}}{x}_{0}-cs\sqrt{{h}_{00}},\hat{{b}_{0}}+\hat{{b}_{1}}{x}_{0}+cs\sqrt{{h}_{00}})$

where $c={t}_{n-2,1-\frac{\alpha}{2}}$ Where these results are found by looking at the shape of the distribution and at $E\left(\hat{{Y}_{0}}\right)$ and $var\left(\hat{{Y}_{0}}\right)$

Predicting observations

"We want to predict the observation $Y}_{0}={\beta}_{0}+{\beta}_{1}{x}_{0}+{\u03f5}_{0$ at a value $x}_{0$"

$E(\hat{{Y}_{0}}-{Y}_{0})=0\text{}\text{and}var(\hat{{Y}_{0}}-{Y}_{0})={\sigma}^{2}(1+{h}_{00})$

Hence a prediction interval is of the form

$(\hat{{b}_{0}}+\hat{{b}_{1}}{x}_{0}-cs\sqrt{{h}_{00}+1},\hat{{b}_{0}}+\hat{{b}_{1}}{x}_{0}+cs\sqrt{{h}_{00}+1})$

asked 2022-04-15

Find the exponential model that fits the points shown in the table. (Round the exponent to four decimal places.)

x | 0 | 5 |
---|---|---|

y | 3 | 1 |

asked 2022-05-01

Sharon draws a random card, from a regular deck of cards, and rolls a regular 6 sided die. What is the probability that Sharon draws a card that is a Heart and rolls a 3?