Solved

Determine Whether the Statement Is True or False

Question 151

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 ​ 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 d<sub>1</sub>, d<sub>2</sub>, 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. ​Solution. Here, we have n=5 and 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 d<sub>1</sub>, d<sub>2</sub>, 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. 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 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 d<sub>1</sub>, d<sub>2</sub>, 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. 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 d<sub>1</sub>, d<sub>2</sub>, 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. 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 d<sub>1</sub>, d<sub>2</sub>, 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. Then, we obtain the normal equations 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 d<sub>1</sub>, d<sub>2</sub>, 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. 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.
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 d<sub>1</sub>, d<sub>2</sub>, 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.
B) It is true, Suppose that we are given two data points 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 d<sub>1</sub>, d<sub>2</sub>, 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. 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.
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 d<sub>1</sub>, d<sub>2</sub>, 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.
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 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 d<sub>1</sub>, d<sub>2</sub>, 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. be made as small as possible. But it is possible only in case when least-squares line passes through at least one data point.

Correct Answer:

verifed

Verified

Unlock this answer now
Get Access to more Verified Answers free of charge

Related Questions

Q146: Find the critical point(s) of the function.

Q147: Determine whether the statement is true or

Q148: Find the critical point(s) of the function.

Q149: Find the critical point(s) of the function.

Q150: Find the equation of the least-squares line

Q152: Find the critical point(s) of the function.

Q153: Find the critical point(s) of the function.

Q154: Find the critical point(s) of the function.

Q155: Find the critical point(s) of the function.

Q156: Find the critical point(s) of the function.

Unlock this Answer For Free Now!

View this answer and more for free by performing one of the following actions

qr-code

Scan the QR code to install the App and get 2 free unlocks

upload documents

Unlock quizzes for free by uploading documents