Question

Find the equation of the regression line for the given data. Then construct a scatter plot of the data and draw the regression line. (The pair of variables have a significant correlation.) Then use the regression equation to predict the value of y for each of the given x-values, if meaningful. The table below shows the heights (in feet) and the number of stories of six notable buildings in a city.

Height, x Stories, y

768 52

628 48

518 45

511 43

491 38

478 35

(a) x=501 ft

(b) x=641 ft

(c) x=318 ft

(d) x=730 ft

Find the regression equation.

ModifyingAbove y with caretyequals=____xplus+left parenthesis ____ right parenthesis

(Round the slope to three decimal places as needed. Round the y-intercept to two decimal places as needed.)

Choose the correct graph to show this

(a) Predict the value of y for

xequals=five hundred and one

Choose the correct answer below.

A. 51

B. 47

C. 40

D. not meaningful

(b) Predict the value of y for

xequals=641

Choose the correct answer below.

A. 47

B. 31

C. 40

D. not meaningful

(c) Predict the value of y for

xequals=318

Choose the correct answer below.

A. 31

B. 47

C. 51

D. not meaningful

(d) Predict the value of y for

xequals=730

Choose the correct answer below.

A. 40

B. 31

C. 51

D. not meaningful

Answer #1

Find X⋅Y and X2 as it was done in the table below.

X | Y | X⋅Y | X⋅X |

768 | 52 | 39936 | 589824 |

628 | 48 | 30144 | 394384 |

518 | 45 | 23310 | 268324 |

511 | 43 | 21973 | 261121 |

491 | 38 | 18658 | 241081 |

478 | 35 | 16730 | 228484 |

Slope = 0.049

Intercept = 15.71

( a ) if x=501 then

y = 15.71 + 0.049 ( 501 )

= 40.259

= **40**

( b ) if x=641 then

y = 15.71 + 0.049 ( 641 )

= 47.119

= **47**

( c ) if x=318 then

y = 15.71 + 0.049 (318 )

= 31.292

= **31**

( d ) if x=730

y = 15.71 + 0.049 (730 )

= 51.48

= **51**

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