Determine Whether the Statement Is True or False

question 73

Multiple Choice

Determine whether the statement is true or false. If it is true, explain why it is true. If it is false, give an example to show why it is false. The least-squares line must pass through at least one data point.

• A) It is false. Example. Find the least-squares line for the data Solution. Here, we have n = 5 and The least-squares line for the data is given by linear equation Y = f(x) = mx + b Where the constants m and b satisfy the normal equations Then, we obtain the normal equations Solving them, we found m = 1, b = 0.4 Therefore, the required least-squares line is y = x + 0.4 The scatter diagram and the least-squares line are shown in the figure. We can see that the line does not pass through any data point.
• B) It is true Suppose that we are given two data points If we try to fit a straight line to these data points, the line will miss the first and the second data points by the amounts d1, d2, respectively. The principle of least squares states that the straight line L that fits the data points best is the one chosen by requiring that the sum of the squares be made as small as possible. But it is possible only in case when least-squares line passes through at least one data point.

Understand how media coverage can affect public perceptions and actions on social issues, including drug problems and urban sprawl.

Distinguish between different types of pornography and their potential impacts on attitudes and behaviors.

Understand how successful actions in politics can influence public perception through selective memory (availability heuristic).

Understand the principles of scientific management and its key innovators.

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Definitions:

Just Noticeable Difference

The minimum difference in stimulus intensity that a specific sense (like sight, hearing, taste, touch, or smell) can detect.

Optic Nerve

The nerve that transmits sensory information from the eye to the brain.

Occipital Lobe

is the region of the brain located at the back of the head, responsible for processing visual information.

Pupils

The opening in the center of the iris of the eye, which regulates the amount of light that enters the eye.