147概念.docx - 147 I Points with second coordinate...

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Unformatted text preview: 147 I Points with second coordinate greater than the first lie above the horizontal rising diagonal; points with second coordinate less than the first lie below the horizontal rising diagonal. If the horizontal and vertical axes have no units, or if they have the same units, then the slope has no units. However, if the axes have different units, the slope must have corresponding units. For example, if the vertical axis is measured in feet and the horizontal in seconds, then the slope is measured in feet per second. Not surprisingly, the units of slope are a rate. Why the Computation Makes Sense' If you picture the points of the scatter diagram plotted on a graph with standard unit scales, the point of averages lands at the origin. Points in the first and third quadrant will have positive products, providing a positive contribution to the average of the products. If these points dominate, i" will be positive. Points in the second and fourth quadrant will have negative products, providing a negative contribution to the average of the products. If these points dominate, 7' will be negative. Pictures May be Deceiving' The appearance of the data in a scatter diagram depends upon the size of the standard unit. The two scatter diagrams belowr both have 1* = .70. The first appears to be more tightly clustered around the SD line because the diagram is drawn with a smaller distance representing the standard unit. If the graphs are scaled so that the standard units coincide, it will become apparent that they have the same correlation. Figure 3. The effem oi changing SDS. The two scatter diagrams have the same correlation coefficient 01' {lit}. The top diagram looks me tightly rlustemd around the SI} line bonus: ils SDs In: smaller. «I a 1" all" at" I- I, a . .3" ‘ I: -: ' - s.;..ki~¢.. a :-' "1' '1‘ '.._* it?!" ' v u.:'J-!:n")"={' "u. 3.1.."- t-tI-‘l 1"- and“ 1 ’x - ill-I" f, t- a ,f.’_ 1—.-—.——.-—-.—-.-—.-—. U 1 I 3 l E l 1‘ I I {a " a. ° .' .: 3J1" a a _ i. 1"!!an :- . . .r‘ - .°. ‘ r:- , --'-':,.«’ 1 ‘ I. a f I. I I. ' in." I t a " If" . u s I. u I" ,4- v! 1 '. .' f...” , ",4“. '.‘ . " "=1. , ' a", r ' t! + o I} II I 3 i I II T I Figure 4. Non-linear association. Regression lines should not be used when there is a non-iinear association between the variables. ...
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