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Finding p-value using linear regression

If I have a linear regression
beta0 + beta1*x1 + beta2*x2

and I find the estimated values of beta1 and beta2, what is the probability I can correctly say that beta1 is the same as zero? i.e., the probability I can correctly say the effect of x2 (i.e. y) is zero?

A:

Assuming $N = 1$:
The linear regression model $y = \beta_0 + \beta_1 x_1 + \beta_2 x_2 + \varepsilon$
has probability distribution:
$$
y \sim \text{i.i.d. Normal}(\beta_0 + \beta_1 x_1 + \beta_2 x_2, \sigma^2)
$$
In this case, the posterior probability of $\beta_1$ is:
$$
P(\beta_1|y) = \frac{f(\beta_1|y)}{\int_{ -\infty}^{\infty} f(\beta_1|y)d\beta_1}
$$
where
$$
f(\beta_1|y) = \frac{1}{\sqrt{2\pi\sigma^2}}\int_{ -\infty}^{\infty} \exp\left[ -\frac{(\beta_1-y)^2}{2\sigma^2}\right] d\beta_1
$$
This is a normal distribution with mean $y$ and standard deviation $\sigma$.
Since $\beta_1$ is a constant, $f(\beta_1|y)$ is a product of two normal distributions, one for the $y$

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Music: Raja Hindustani / Watch Online; Raja Hindustani (1996) Hindi Movie Playlist: Hu Song Yili; Лондон Сквир Кассов (Музыка) - .
Raja Hindustani (1996) Hindi Movie Soundtrack: Hu Song Yili (2:24). Released : 1996  .Field of the Invention
The present invention relates to an electronic device, and more particularly, to an electronic device and a method of controlling a touch input in the electronic device.
Discussion of the Related Art
A touchscreen is a kind of input device that enables a user to directly and intuitively input information or control devices through a screen without a physical keyboard or mouse. The touchscreen may be attached to a display device, such as a mobile phone, a tablet computer, a laptop computer, and so on.
The touchscreen may receive a user’s input such as a touch, pressure, a swipe or an etching by a user through a touch pen or a user’s finger.
A touchscreen module may be applied to various products. For example, there is an electronic device including a touchscreen module applied thereto.
The touchscreen module may be mounted on a touchscreen sensor in various forms, such as a resistive type, a capacitive type, an electromagnetic type, and an optical type.
The touchscreen has some advantages, such as a user interface in a simple shape, a non-contact type, and a small and thin form factor. However, there is a disadvantage that the touchscreen needs a separate input device such as a physical keyboard or mouse.
As a touch input method of overcoming the disadvantage of the touchscreen, a capacitive type has been introduced.
The capacitive type touch screen detects a change in a capacitance by being touched by a human body to control a device.
The capacitive type touch screen may sense the touch through an electrical or electrostatic coupling. Accordingly, a user can interact with a device more intuitively and exactly without using a physical keyboard or mouse.
The capacitive type touch screen may include a resistance film type and a projected capacitance type. The resistance film type touch screen may include a resistance film and a glass substrate. The projected capacitance type touch screen may include a glass substrate and a transparent conductive film on the glass substrate.
The projected capacitance type touch screen may detect a change in capacitance generated by the
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