# Chapter 1. Facts about the Least-Squares Regression

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0:34

### Question 1.1

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Correct. This is a correct statement.
Incorrect. This is a correct statement.
2
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### Question 1.2

3xMJuMbnLvEdWJP/lY2WkLVWtu+5sB19A2j56G+1GVNejuEgVMtqJHiR4/Z0m9s3LhwRxGRUJ0YtZ3Wav3xvMsL0u0O6Oby0B0MyCFhZ/pj8CLMJZ2i0tuywQ/0enoqcE9HAJrDNBYDdZLRLaZFi5zMHKhMkZGO/rgIQutVrUsS2uxhxrM9/uo30oXm2IjPdsRY7kwKKbxcOqoMuIAcVpwD7Tdk=
Correct. The sign of correlation tells us direction and where it is on a scale from zero to one tells us the strength of the relationship.
Incorrect. The sign of correlation tells us direction and where it is on a scale from zero to one tells us the strength of the relationship.
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### Question 1.3

bK7TshY83bSSP+3lUH6nZf75gs/zM269DeddqoNM5NXl+sUsPmHn/t9/kSfsJsJITYZnGmtbIzw5z5ZLMFv5ix+NBmGoaLHdf1V4xwTdo0cY6T0v3fUPHYIGfyOd67/25kSrgmSFWO/FTyxlc/zIxwqfzZWl0QYjm4xd544HDBxwsa6rxzzMrdyZKETQV8yz/OiwMA0zEF6KgcLdpChJZDGdXIQ=
Correct. Regression gives us a formula for the line: $$\widehat{y} = a + bx$$.
Incorrect. Regression gives us a formula for the line: $$\widehat{y} = a + bx$$.
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1:33

### Question 1.4

cW7d12XfVZp2hUdiDiT4zugOLchdT7K1Slmly4ExUVpyLqApS12+SChxE31wp3xVbWlVCvRQ7mH4nTM8QTK5ug2SGEkRRgqBEzgdu115tEZK+gGf31foKXEqUxhVDv8j/Q2vdMltwN3Lg2sb
Correct. X and Y can be interchanged in correlation, but not in the formula for a regression line: $$\widehat{y} = a + bx$$.
Incorrect. X and Y can be interchanged in correlation, but not in the formula for a regression line:$$\widehat{y} = a + bx$$.
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### Question 1.5

mDMKzpKpAhp2pAj5l1j0mDQjqI3lqeW2kvqP4w0Yoyx3CYwqR+pq2rAv7PXQPh2jwENndgfg9Zp0IBGD9rKZKis8qTBzqfJgYy9GnJRDSC7EGLx6mvZq/yYutU977+apv6Eg8bkj4jEzthan
Correct. X and Y can be interchanged in correlation, but not in the formula for a regression line: $$\widehat{y} = a + bx$$.
Incorrect. X and Y can be interchanged in correlation, but not in the formula for a regression line: $$\widehat{y} = a + bx$$.
2
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### Question 1.6

fPJy9mH2sFYDJGtjLb7DKjgryFjZyO1ipvNRgQyTDg/R0Jw+sM2T7nGDZNSpkB8eLZ+OBpXUnwA96AeXtfuIHCiBa35BE5UAfIfQbUig1VQA5hpi17JKBs6t88iBHvYw66hTt3o6z0RU2budLdIQLZBROHs+HoXG
Correct. X and Y can be interchanged in correlation, but not in the formula for a regression line: $$\widehat{y} = a + bx$$.
Incorrect. X and Y can be interchanged in correlation, but not in the formula for a regression line: $$\widehat{y} = a + bx$$.
2
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2:53

### Question 1.7

WNANujIyct9SUJj9Y11fJTLORpfz/9QYMNJolyT9dapqbSXHJpoeqMPkKe9u413EqlL5Rt3EN7U9AjtaMDfKdyTcfrnoZb6qgwQxHFbfXB1TnXLQeTC59w==
Correct. This is a correct statement.
Incorrect. This is a correct statement.
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### Question 1.8

Z5ps2xfAoDVOujJ6JlpuVG75xF5gfRSgSL4f9EeovoET7bbgqeWsOnoknyqFgKS0UBHY3FjmhzpveXy1wbSsTWFV0g19FCBb0YVrD+vywIY87lmV4t+CzXmHV9Y=
Correct. This is a correct statement.
Incorrect. This is a correct statement.
2
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### Question 1.9

C5fsRaeR/+TFqaF3qU5PsDRPXJPw865AAfNsOijbAKXLD8UuNDPfqycZZqHN4e9lI5IsCDkJSPtlLPp3ZbQR+/ruKdl5a2lAXdgHWJovzrm+gqugvpr1Oomz3+TWYDOTn74RmA==
Correct. This is a correct statement.
Incorrect. This is a correct statement.
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### Question 1.10

2JVayptw8dPdVmcQbXCEznwe0vHm7aTzEU9sPUbApTYwNWISgUKdSowCIKyOWxtY0Pvip6K6bIeJcJaUbzDQQuYS6uXu+SnaXv/eKzJrq1ShYpqqVzwnQsBjlKcWpQL3EGTCa/oQqZgtjr2pIirUxVIBgPhT6Z5Rnu/dzQaIfXkCGZPiB9GkrA==
Correct. If correlation, r, is negative, then slope will always be negative.
Incorrect. If correlation, r, is negative, then slope will always be negative.
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### Question 1.11

mLcIZr8UX4ImqXWWIpx87L1/tKQIsucUMFcLJgz5YBihuYN8+icU0cThjOlx8dBlV8slMbrOXzkNjUSZLh1pBoOY7l3Shge0RywTMAOEpAWlAaAgNNU+7I2k75MKei5Etp39Z4Ai5y7EagHTALSxDQ==
Correct. Knowing the value of slope only tells us the direction of r; the value of slope tells us nothing about the value of r.
Incorrect. Knowing the value of slope only tells us the direction of r; the value of slope tells us nothing about the value of r.
2
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3:18

### Question 1.12

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Correct. This is a correct statement.
Incorrect. This is a correct statement.
2
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7:07

### Question 1.13

kt9EJggLkkGqojL95O+uD1yJqzxO/avaRhHLPECNcY/WwBk0xxBC880yq/SahFSeCiaXJLEdVsyU38kolfSRuyIlxXRE6FjNYf3dCvOij5AtsoK31oXzDTu5JV7R3JNusq/iFrUTSnP9S14eFltj1byWTWDYOXDggQu2u0CwlvekTnIWsSIahH8ktvDRzZY+nkrA2bhTTGFsUnQX
Correct. When all of the data points are on the regression line, r is either –1.0 or +1.0. So, r2 will be 100%.
Incorrect. When all of the data points are on the regression line, r is either –1.0 or +1.0. So, r2 will be 100%.
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### Question 1.14

We27MUi1Gw+Md79mufz9UgUa8t0V17S8oTZFGIrU4mT1b7tO/HUuA+J+nCTIeKuF5cRN94RFZyJ4nnmHYDlwiiSDTTNKgmkjLwiknoqRWXZ+Q57huxg80tBSKX4+qIIaTG+V6vp95oDAK2QY1lSTJRsienfPrAhj1PpoheZa/226+wBgMwe4+Q4UuAk/lG8Ryn2qzr1FBmabffMst4vlJTeFa4Ft4hT2WUjwKBWkRFMaR+B532CcIUcdYpMFdf93P3EgEjEONjwoTzT+2JWoa/vTrPoWz+MGRBZj/ekLoLIWrUzOhE5slIVZEvH7FWGrsyYUyFqcsO2ZRBhu2r1nWO/obQ/1C6LJg4RRTlTjykA=
Correct. When there is no relationship between X and Y, the cloud of data should resemble a hamburger bun.
Incorrect. When there is no relationship between X and Y, the cloud of data should resemble a hamburger bun.
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### Question 1.15

Correct. We expect the data points to be close to the regression line when r2 is close to 100% and scattered when r2 is close to 0%.
Incorrect. We expect the data points to be close to the regression line when r2 is close to 100% and scattered when r2 is close to 0%.
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### Question 1.16

p8ThPttaQmicvdQ83J0tPUP3TB5fAwboVZUwtdlD6YgW0EUyMS+QvyRc/eAuasolniQDC5GCXmU3VEUpFUVmu/pQoCnA7WwMIH2ejt0cN498kEmypI2WrnMWWljdK+c+eTyeEZDBK7+DwCJQbWXOcsiPsnrDZpg7v44TRv9Hnn/yafF/57M8O3BT8TsEqG3qACK7kEaLIfTAS3wHtDCyXHJtr+Utn0e9pDbwnPPxD2PFHaa2jciEQyBEgRPFeNsPEurgsIBgYElaqtJtERucarxLDnutKS73
Correct. In statistics we are very concerned about variation and r2 tells us about the variation in y.
Incorrect. In statistics we are very concerned about variation and r2 tells us about the variation in y.
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8:22

### Question 1.17

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Correct. This is a correct statement.
Incorrect. This is a correct statement.
2
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9:53

### Question 1.18

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Correct. This is a correct statement.
Incorrect. This is a correct statement.
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### Question 1.19

8ctNB8KxDNe4ysICixCDpHlYc1GVTl2glLxt2KPF2dSQklZSfRZOkAkdZ/F5fTRjgPAboPi1TB6Pa/igxslEJl0PS97cvcbzpVqnivUWLrgMhcDdnTCTjOoF9JmPOiab2rB14gZV7g7Bxfacn91qsgswR4q3AWPBD4Q17A==
Correct. If r2 is really close to 100%, then there is very little unexplained variation.
Incorrect. If r2 is really close to 100%, then there is very little unexplained variation.
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10:31

### Question 1.20

5EYqF8+vrYu80v4RWyj2Ub3e2St4zYsf8x90zm1/Pb1SpIRV/Q8jW6dlx/lkF76EvmBwf1yI2jRsrV0mtwaIyW62Z6kF/B7VJQxIU4bSrn0OaL5AGysxxJ5JiPH9i7bsouxYHRO78SBISDoY2TieazMwf2r8KxvPq4u1vDIIPGY=
Correct. r2 is a measure of the fraction of variation in the y’s that is explained by x. It does not tell us the fraction of y values that are exactly predicted as most are not, even when r2 is close to 100%.
Incorrect. r2 is a measure of the fraction of variation in the y’s that is explained by x. It does not tell us the fraction of y values that are exactly predicted as most are not, even when r2 is close to 100%.
2
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12:34

### Question 1.21

1D2HnZwwlxc2MEVwEH+fArNsHnuP0LMKWhJcWsrr4y4jo39Yn40Mb/ps1++u5CvbCh31rEUHEh87DygSllQ8a+/vgtBqGciwn9cJWTwzjh9WhNL0IPpbx1+QxOSywByh2EqnCzYcrkG4u8ABAfzLoEUuNuXw9sxMSwUo4gtH2TEBNfByJmIByi2k637SxIzGWjooIDKJuD29ciS7dmQprJFlTq8KymFW4vbk+uCLFNAwImRU
Correct. The variability of the y’s about their mean $$\overline{y}$$ is called the total variation in y. The variability of the y’s about the regression line is a measure of the prediction errors (or residuals).
Incorrect. The variability of the y’s about their mean $$\overline{y}$$ is called the total variation in y. The variability of the y’s about the regression line is a measure of the prediction errors (or residuals).
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### Question 1.22

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Correct. If the prediction errors are small, then there is very little unexplained variation in the y’s and r2 is close to 100%. On the other hand, if the prediction errors are large, then there is a lot of unexplained variation and r2 is close to 0%.
Incorrect. If the prediction errors are small, then there is very little unexplained variation in the y’s and r2 is close to 100%. On the other hand, if the prediction errors are large, then there is a lot of unexplained variation and r2 is close to 0%.
2
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13:55

### Question 1.23

Wkd1eYN9pljQ+fioDDypkZhfqYfH+wn6h9YwsqpxQZcp7yA9Gb1DK5Y0NUEhbsPtMNZwWvYh2kK3mJG+q5JVokWtmrCiQKqpP5yvo2e43B2UhbhfSw6+AGdIaS1mjPp2d1n+P5snui1c3HQzcYgJ3rn09uDrSqLAakal1TNVDH8N7Sbsr8sb6xCATvxbnMeztowCf+7W4pTPtEkdXLW4CvHKHN0D7l/qN1W2qyn/4DHc4nxcAtRzlRC5pQFrFRTUZI+BinzRQ+hEvmHO2DAhCC0pra6ZTRa+6p7HIjpRZ5hVe+GLmcwFsaTc+XyogUPv+xk6UYcigXIJZS3YjIK9lyr/NKfbuCMeXxt5vPRk08mzeU2CiRcMXiNs8U87lWZHmMl4gdd7cqZj0AgCD+32syaN1psI1/8+8lB85FnmDH90UfkmkO07TphogDM=
Correct. r2 tells us the percentage of variation in y that is explained by x. And the closer r2 is to 100%, the greater the variation in y that gets explained. So an r2 of 89% tells us that more variation in y is explained than when r2 is 47%.
Incorrect. r2 tells us the percentage of variation in y that is explained by x. And the closer r2 is to 100%, the greater the variation in y that gets explained. So an r2 of 89% tells us that more variation in y is explained than when r2 is 47%.
2
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### Question 1.24

JgYxdZhtiKcQH+5rnOuauWTZJsQPAsStm3/zSryiN8KltUm/0GF2P7n1DZxAubTRtVsTo3YVEzRf27sNlBswEioon0JRXJf52EwJjlXDSyazlhLm2PUxJDV+NmeylQMyJB8D3+1T2oBdo0dqoJE/rLJP7a9jwH7ZHRyBYtmUb1+w6pnn33L4ktQ8+V1+WqTLEuXfdr9eACoRgYBla3uXzZqaFF9mAlZK5/NHCOU6CEfGvMOeEfv7B3PgfaHMoTkdAcpNKZTq3CnoixYW3v25QikPIFG7rTh1LfRul8qjAks=
Correct. r2 tells us the percentage of variation in y that is explained by x. So, r2 = (0.90)2 = 0.81 or 81% of the variation in blood alcohol content can be explained by number of beers consumed.
Incorrect. r2 tells us the percentage of variation in y that is explained by x. So, r2 = (0.90)2 = 0.81 or 81% of the variation in blood alcohol content can be explained by number of beers consumed.
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