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3. Computing the regression line and making predictions Suppose you are a dolphin trainer at SeaWorld. You teach the dolphins by rewarding them with fish treats after each successful attempt at a new trick. The following table lists the dolphins, the number of treats per success given to each, and the average number of attempts necessary for each to learn to perform the tricks. Dolphin Number of Treats Number of Attempts Diana 2 6 Frederick 4 5 Fatima 1 8 Marlin 3 5 You can use the preceding sample data to obtain the regression line, where ? is the predicted value of Y: ? = bX + a One formula for the slope of the regression line is as follows: b = SP / SSx To calculate the slope, first calculate SP and SSx: SP = ___, and SSx = _. (Hint: For SP use the computational formula and for SSx use the definitional formula.) The slope of the regression line is _, and the Y intercept of the regression line is ___.

          3. Computing the regression line and making predictions
Suppose you are a dolphin trainer at SeaWorld. You teach the dolphins by rewarding them with fish treats after each successful attempt at a new trick. The following table lists the dolphins, the number of treats per success given to each, and the average number of attempts necessary for each to learn to perform the tricks.

Dolphin Number of Treats Number of Attempts
Diana 2 6
Frederick 4 5
Fatima 1 8
Marlin 3 5

You can use the preceding sample data to obtain the regression line, where ? is the predicted value of Y:
? = bX + a
One formula for the slope of the regression line is as follows:
b = SP / SSx
To calculate the slope, first calculate SP and SSx:
SP = _____, and SSx = _____.
(Hint: For SP use the computational formula and for SSx use the definitional formula.)
The slope of the regression line is _____, and the Y intercept of the regression line is _____.

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3. Computing the regression line and making predictions
Suppose you are a dolphin trainer at SeaWorld. You teach the dolphins by rewarding them with fish treats after each successful attempt at a new trick. The following table lists the dolphins, the number of treats per success given to each, and the average number of attempts necessary for each to learn to perform the tricks.

Dolphin Number of Treats Number of Attempts
Diana 2 6
Frederick 4 5
Fatima 1 8
Marlin 3 5

You can use the preceding sample data to obtain the regression line, where ? is the predicted value of Y:
? = bX + a
One formula for the slope of the regression line is as follows:
b = SP / SSx
To calculate the slope, first calculate SP and SSx:
SP = , and SSx = .
(Hint: For SP use the computational formula and for SSx use the definitional formula.)
The slope of the regression line is , and the Y intercept of the regression line is .

Added by Jacob W.

Elementary Statistics a Step by Step Approach

Allan G. Bluman 9th Edition

Instant Answer

Solved by Expert Sri K

06/14/2022

Step 1

This data is missing in the text provided. Once we have the data, we can calculate SP (the sum of the products of the differences from the mean) and SSx (the sum of the squares of the differences from the mean for the x-values). The formula for SP is Σ[(x - mean Show more…

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Computing the regression line and making predictions Suppose you are a dolphin trainer at SeaWorld. You teach the dolphins by rewarding them with fish treats after each successful attempt at a new trick. The following table lists the dolphins, the number of treats per success given to each, and the average number of attempts necessary for each to learn to perform the tricks. Number of Treats Number of Attempts Dolphin Diana Frederick Fatima Marlin You can use the preceding sample data to obtain the regression line where Y is the predicted value of Y: bX + a. One formula for the slope of the regression line is as follows: SP / SSx. To calculate the slope, first calculate SP and SSx: SP = SSx = (Hint: For SP, use the computational formula and for SSx, use the definitional formula.) The slope of the regression line is and the intercept of the regression line is

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Transcript

00:03 Hello, students, welcome.

00:04 We have a question here and here we need to use the regression line to estimate the trades and it would be like to learn the tricks.

00:24 And now we have to find the y cap for x is equal to 5 and we need to find the appropriate response over from the given option.

00:35 First of all, we have to create a table for the given observation for x, one column is x, second column will be y, then we have x into y as third column.

00:46 Lastly, we will find the value for x square into the fourth one.

00:51 So let's start solving.

00:53 I have made this table by using excel.

00:55 Here is the table.

00:57 You can see this is the value of x, y, xy, and x square.

01:02 And in this column, i have added all the values in this row.

01:07 I'm sorry, all the values into the column.

01:10 This is summation of x.

01:12 Here we have summation of y.

01:14 Then submission of xy, sum of all values, and submission of x squared.

01:20 And our sample size is 4 because we have total 4 observation.

01:24 So here, the regression line is.

01:37 Standard notification is y cap is equal to a plus b x and now from here we will be equal to sp upon s s x this is the formula for finding b so first of all let's find sp sp is equal to submission of x y minus submission of x multiplied by submission of x by submission of y and this full value has to be divided by n.

02:17 So let's find the value for this.

02:22 First of all, for sp.

02:24 So all the values into this column, we have sum as 65.

02:29 Then for submission of x, submission of x is equal to 10 multiplied by 28.

02:38 Sample size n is equal to 4.

02:40 So when we calculate this value, this sp will be equal to minus y so we are having our first value to find b s p is here so now let's find out s x and its formula is sim of all observation x into y minus submission of x squared divided by n so this will be as 30 minus 10 whole square divided by sample sizes 4...

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