Lesson test: Fitting a line

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Fitting a line

1.[2p]
What does least squares minimise?

The sum of squared vertical distances from the points to the line

Correct

The sum of perpendicular distances from the points to the line

The answer is: The sum of squared vertical distances from the points to the line

The largest distance from any point to the line

The answer is: The sum of squared vertical distances from the points to the line

The number of points not on the line

The answer is: The sum of squared vertical distances from the points to the line

2.[2p]
Fathers and sons both have standard deviation 2.7 inches and correlate 0.51. What is the slope of the line predicting son from father?

CorrectNot quite: 0.51

3.[2p]
The fitted least squares line always passes through the point $(\overline{x}, \overline{y})$ .

True

Correct

False

The answer is: True

4.[2p]
For Anscombe's first dataset, $S_{x y} = 55.01$ and $S_{x x} = 110$ . What is the slope, to three decimal places?

CorrectNot quite: 0.5

5.[3p]
The same fit has residual sum of squares 13.763 and total sum of squares 41.273. What is $r^{2}$ , to three decimal places?

CorrectNot quite: 0.667

6.[3p]
The residual standard deviation is 1.237 and $S_{x x} = 110$ . What is the standard error of the slope, to four decimal places?

CorrectNot quite: 0.1179

7.[2p]
Why is the residual sum of squares divided by $n - 2$ ?

Two parameters were estimated from the data before the residuals were formed

Correct

There are two variables in the model

The answer is: Two parameters were estimated from the data before the residuals were formed

Two observations are always discarded

The answer is: Two parameters were estimated from the data before the residuals were formed

The slope and the correlation are computed separately

The answer is: Two parameters were estimated from the data before the residuals were formed

8.[3p]
Match each residual pattern to what it indicates.

A curve in the residuals
A widening funnel
One far-off point at extreme $x$
No pattern at all

the error variance is not constant
high leverage on the slope
the relationship is not linear
the model assumptions look reasonable

Show the answer

A curve in the residuals: the relationship is not linear A widening funnel: the error variance is not constant One far-off point at extreme $x$ : high leverage on the slope No pattern at all: the model assumptions look reasonable

9.[3p]
Which of these can produce a significant slope with no causal content?

Select all that apply

A third variable driving both $x$ and $y$

Correct

The causal arrow running from $y$ to $x$

Correct

A sample selected on a combination of $x$ and $y$

Correct

A residual sum of squares that is too small

The answer is: A third variable driving both $x$ and $y$ , The causal arrow running from $y$ to $x$ , A sample selected on a combination of $x$ and $y$

1.[2p] What does least squares minimise?

2.[2p] Fathers and sons both have standard deviation 2.7 inches and correlate 0.51. What is the slope of the line predicting son from father?

3.[2p] The fitted least squares line always passes through the point (x‾,y‾).

4.[2p] For Anscombe's first dataset, Sxy=55.01 and Sxx=110. What is the slope, to three decimal places?

5.[3p] The same fit has residual sum of squares 13.763 and total sum of squares 41.273. What is r2, to three decimal places?

6.[3p] The residual standard deviation is 1.237 and Sxx=110. What is the standard error of the slope, to four decimal places?

7.[2p] Why is the residual sum of squares divided by n−2?

8.[3p] Match each residual pattern to what it indicates.

9.[3p] Which of these can produce a significant slope with no causal content?

1.[2p]
What does least squares minimise?

2.[2p]
Fathers and sons both have standard deviation 2.7 inches and correlate 0.51. What is the slope of the line predicting son from father?

3.[2p]
The fitted least squares line always passes through the point $(\overline{x}, \overline{y})$ .

4.[2p]
For Anscombe's first dataset, $S_{x y} = 55.01$ and $S_{x x} = 110$ . What is the slope, to three decimal places?

5.[3p]
The same fit has residual sum of squares 13.763 and total sum of squares 41.273. What is $r^{2}$ , to three decimal places?

6.[3p]
The residual standard deviation is 1.237 and $S_{x x} = 110$ . What is the standard error of the slope, to four decimal places?

7.[2p]
Why is the residual sum of squares divided by $n - 2$ ?

8.[3p]
Match each residual pattern to what it indicates.

9.[3p]
Which of these can produce a significant slope with no causal content?