1. The absolute magnitude of the reduction in variation of Y when time is introduced into the regression model can be calculated by subtracting the variance of Y in the original model from the variance of Y in the new model.
2. The relative reduction can be calculated by dividing the absolute magnitude by the variance of Y in the original model.
3. The latter measure is called the coefficient of determination or R-squared and represents the proportion of variance in Y that can be explained by the regression model.
When time is introduced into a regression model, it can have an impact on the variation of the dependent variable Y. The absolute magnitude of this reduction in variation can be measured by calculating the difference between the variance of Y in the original model and the variance of Y in the new model that includes time. The relative reduction in variation can be calculated by dividing the absolute magnitude of the reduction by the variance of Y in the original model.
The latter measure, which is the ratio of the reduction in variation to the variance of Y in the original model, is called the coefficient of determination or R-squared. This measure represents the proportion of the variance in Y that can be explained by the regression model, including the independent variable time. A higher R-squared value indicates that the regression model is more effective at explaining the variation in Y.
To know more about magnitude visit:
brainly.com/question/2596740
#SPJ11
Consider three identical metal spheres, a, b, and c. sphere a carries a charge of 5q. sphere b carries a charge of -q. sphere c carries no net charge. spheres a and b are touched together and then separated. sphere c is then touched to sphere a and separated from it. lastly, sphere c is touched to sphere b and separated from it.
required:
a. how much charge ends up on sphere c?
b. what is the total charge on the three spheres before they are allowed to touch each other?
a. Sphere c ends up with a charge of -3q.
b. The total charge on the three spheres before they are allowed to touch each other is 5q - q = 4q.
a. When spheres a and b are touched together and then separated, charge is transferred between them until they reach equilibrium. Since sphere a has a charge of 5q and sphere b has a charge of -q, the total charge transferred is 5q - (-q) = 6q. This charge is shared equally between the two spheres, so sphere a ends up with a charge of 5q - 3q = 2q, and sphere b ends up with a charge of -q + 3q = 2q.
When sphere c is touched to sphere a and separated, they share charge. Sphere a has a charge of 2q, and sphere c has no net charge initially. The charge is shared equally, so both spheres end up with a charge of q.
Similarly, when sphere c is touched to sphere b and separated, they also share charge. Sphere b has a charge of 2q, and sphere c has a charge of q. The charge is shared equally, so both spheres end up with a charge of (2q + q) / 2 = 3q/2.
Therefore, sphere c ends up with a charge of -3q (opposite sign due to excess electrons) and the total charge on the three spheres before they are allowed to touch each other is 5q - q = 4q.
learn more about spheres here:
https://brainly.com/question/22849345
#SPJ11
The net force on any object moving at constant velocity is a. equal to its weight. b. less than its weight. c. 10 meters per second squared. d. zero.
The net force on any object moving at constant velocity is zero. Option d. is correct .
An object moving at constant velocity has balanced forces acting on it, which means the net force on the object is zero. This is due to Newton's First Law of Motion, which states that an object in motion will remain in motion with the same speed and direction unless acted upon by an unbalanced force. This is due to Newton's first law of motion, also known as the law of inertia, which states that an object at rest or in motion with a constant velocity will remain in that state unless acted upon by an unbalanced force.
When an object is moving at a constant velocity, it means that the object is not accelerating, and therefore there must be no net force acting on it. If there were a net force acting on the object, it would cause it to accelerate or decelerate, changing its velocity.
Therefore, the correct answer is option (d) - the net force on any object moving at a constant velocity is zero.
To know more about Net force refer here :
https://brainly.com/question/14361879
#SPJ11
Calculate the angular separation of two Sodium lines given as 580.0nm and 590.0 nm in first order spectrum. Take the number of ruled lines per unit length on the diffraction grating as 300 per mm?
(A) 0.0180
(B) 180
(C) 1.80
(D) 0.180
The angular separation of two Sodium lines is calculated as (C) 1.80.
The angular separation between the two Sodium lines can be calculated using the formula:
Δθ = λ/d
Where Δθ is the angular separation, λ is the wavelength difference between the two lines, and d is the distance between the adjacent ruled lines on the diffraction grating.
First, we need to convert the given wavelengths from nanometers to meters:
λ1 = 580.0 nm = 5.80 × 10⁻⁷ m
λ2 = 590.0 nm = 5.90 × 10⁻⁷ m
The wavelength difference is:
Δλ = λ₂ - λ₁ = 5.90 × 10⁻⁷ m - 5.80 × 10⁻⁷ m = 1.0 × 10⁻⁸ m
The distance between adjacent ruled lines on the diffraction grating is given as 300 lines per mm, which can be converted to lines per meter:
d = 300 lines/mm × 1 mm/1000 lines × 1 m/1000 mm = 3 × 10⁻⁴ m/line
Substituting the values into the formula, we get:
Δθ = Δλ/d = (1.0 × 10⁻⁸ m)/(3 × 10⁻⁴ m/line) = 0.033 radians
Finally, we convert the answer to degrees by multiplying by 180/π:
Δθ = 0.033 × 180/π = 1.89 degrees
Rounding off to two significant figures, the answer is:
(C) 1.80
To know more about angular separation, refer
https://brainly.com/question/30365113
#SPJ11