How much should a healthy Shetland pony weigh? Let x be the age of the pony (in months), and let y be the average weight of the pony (in kilograms).x36122026y6095140160189(a) Make a scatter diagram of the data and visualize the line you think best fits the data.  Flash Player version 10 or higher is required for this question. You can get Flash Player free from Adobe's website. (b) Would you say the correlation is low, moderate, or strong? lowmoderate    strongWould you say the correlation is positive or negative? positivenegative    (c) Use a calculator to verify that     x = 67,     x2 = 1265,     y = 644,     y2 = 93,546, and     xy = 10,544. Compute r. (Round your answer to three decimal places.)  As x increases from 3 to 26 months, does the value of r imply that y should tend to increase or decrease? Explain your answer. Given our value of r, y should tend to increase as x increases.Given our value of r, we can not draw any conclusions for the behavior of y as x increases.Given our value of r, y should tend to remain constant as x increases.Given our value of r, y should tend to decrease as x increases.

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Asked Jul 18, 2019
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How much should a healthy Shetland pony weigh? Let x be the age of the pony (in months), and let y be the average weight of the pony (in kilograms).

x 3 6 12 20 26
y 60 95 140 160 189
(a) Make a scatter diagram of the data and visualize the line you think best fits the data. 

 
Flash Player version 10 or higher is required for this question. 
You can get Flash Player free from Adobe's website.

 


(b) Would you say the correlation is low, moderate, or strong? 
low
moderate    
strong

Would you say the correlation is positive or negative? 
positive
negative    

(c) Use a calculator to verify that 
   
 
 
x = 67,
 
   
 
 
x2 = 1265,
 
   
 
 
y = 644,
 
   
 
 
y2 = 93,546,
 and 
   
 
 
xy = 10,544.
 

Compute r. (Round your answer to three decimal places.) 
 

As x increases from 3 to 26 months, does the value of r imply that y should tend to increase or decrease? Explain your answer. 
Given our value of ry should tend to increase as x increases.
Given our value of r, we can not draw any conclusions for the behavior of y as x increases.
Given our value of ry should tend to remain constant as x increases.
Given our value of ry should tend to decrease as x increases.
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Expert Answer

Step 1

Part (a):

The scatter diagram, along with the best fitted line (least-squares regression line) for the data is as follows:

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Scatterplot of y vs x 200 175 150 125 100 75 50 0 10 15 20 25 309

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Step 2

Part (b):

All the points fall very close to the straight line in the graph, in such a way, that as x increases, y also increases.

Thus, the correlation is strong and positive.

Step 3

Part (c):

Here, x, x2, y, y2, and xy are the sums of X, X2 Y, Y2, and XY, respectively.

Using calculator, it is verified that:

x = (3 + 6 + 12 + 20 + 26) = 67.

x2 = (32 + 62 + 122 + 202 + 262) = 1,265.

y = (60 + 95 + 140 + 160 + 189) = 644.

y2 = (602 + 952 + 1402 + 1602 + 1892) = 93,546.

xy = (3×60) + (6×95) + (12×140) + (20×160) + (26×189) = 10...

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nxy)-(x)(y) (*)(x] [n(*)-(y [5x10,544][67x 64] ESx1.265-672x[5x93.546}-644 52,720 45,148 6,325-4,489x[467,730-414,736] 9,572 V1,836 x52,994 9,572 9,863.923 0.970

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