# Least squares estimate, regression model and corresponding residuals

S

#### silverjlp

Hello,
I am a statistics student. I have a Minitab assignment. My professor is making us learn Minitab on our own - really. I desperately need help and step by step help. I know very little about Minitab.

Here are the questions:
It is suspected that the rating is related to the average number of yards gained per pass attempt (x).
(a) Calculate the least squares estimates of the slope and intercept. What is the estimate of σ2 (ohm squared)? Graph the regression model.
(b) Find an estimate of the mean rating if a quarterback averages 7.5 yards per attempt.
(c) What change in the mean rating is associated with a decrease of one yard per attempt?
(d) To increase the mean rating by 10 points, how much increase in the average yards per attempt must be generated?
(e) Given that x is 7.21 yards, find the fitted value of x and the corresponding residual.​

Here is the data:

Yds Rating
8.39 105.5
7.67 97.4
7.66 96.9
7.98 96.2
7.21 95.0
7.53 93.8
8.01 92.7
7.66 91.4
7.21 90.2
7.16 89.4
7.93 87.7
7.10 87.5
6.33 87.0
6.76 86.4
6.86 86.4
7.35 86.0
7.22 85.4
7.94 84.7
6.41 84.3
6.77 81.7
6.65 81.0
6.94 80.3
6.45 80.2
7.04 80.1
6.39 79.6
6.58 77.1
6.21 76.0
7.17 73.7
6.34 72.6
6.18 71.4
5.12 70.0
5.71 66.5

I have found in Stat - Regression - Regression - Fit Regression Model, but what is in the responses and what is in continuous predictor?

You are not doing my homework for me, even if you answer step by step.

I appreciate all you can offer.

Last edited by a moderator:

#### Miner

##### Forum Moderator
Recall from high school the equation of a line is: y = mx + b.
• y is the response
• m is the slope (in the Minitab output, this will be the Coef[ficient] for the continuous predictor)
• x is the continuous predictor
• b is the y intercept (in the Minitab output, this will be the Coef[ficient] for the Constant)

See how far you can get with this info, and post back if you have more questions.

S

#### silverjlp

Alright, that looks good. I did the 4 in one graph.

We're off to a start- THANK YOU....I have a formula for the line and the graph of the regression model.

What is the estimate of σ2 (ohm squared - the variance)?

plus b-d? am I just changing the source data and making new graphs each time?

I have no ideas on part e.

S

#### silverjlp

nevermind, estimate the ohm squared is different than just the variance. I already completed this problem by hand. Minitab answers should match.

It's 27.24 - but I don't get the using Minitab

S

#### silverjlp

So Mean Squares Error = Variance. I learned something new.......

Still taking a crack at b-e.....

Thank you for everything so far......

I would be so appreciative of help still.

#### Miner

##### Forum Moderator
nevermind, estimate the ohm squared is different than just the variance. I already completed this problem by hand. Minitab answers should match.

It's 27.24 - but I don't get the using Minitab
Note: It is sigma squared, not ohm squared.

You can also obtain the 27.24 by squaring the s = 5.21874. S is the sample standard deviation, while sigma is the population standard deviation.

#### Miner

##### Forum Moderator
Here are the questions:
It is suspected that the rating is related to the average number of yards gained per pass attempt (x).

(b) Find an estimate of the mean rating if a quarterback averages 7.5 yards per attempt.
(c) What change in the mean rating is associated with a decrease of one yard per attempt?
(d) To increase the mean rating by 10 points, how much increase in the average yards per attempt must be generated?
(e) Given that x is 7.21 yards, find the fitted value of x and the corresponding residual.​

(b) Substitute 7.5 for Yds in your equation.
(c) Hint: Use the slope.
(d) Substitute 10 for the Rating in your equation and solve for Yds.
(e) In Minitab, select the Storage button, check the Residuals box, run the analysis, go to the Worksheet, find the row with 7.21 Yds and look at the corresponding RESI (residual). For the fitted value, substitute 7.21 for Yds in the equation.​

#### Statistical Steven

##### Statistician
Super Moderator
(e) Given that x is 7.21 yards, find the fitted value of x and the corresponding residual.[/LEFT]
Should be fitted value of Y

S

#### silverjlp

Thanks, I don't know why I said Ohm. Silly me!

Ok, I am down to (e) Given that x is 7.21 yards, find the fitted value of x and the corresponding residual.

You said In Minitab, select the Storage button, <--- How do I get there?

I don't know how to do the fitted value of y

I tried looking for 7.21 in my "session" output, but don't see it.

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