Scatterplots Level 1
Height of
Father (in)
62
63
Height of
Woman (in)
60
60
65
65
66
60
63
65
66
67
68
66
61
63
68
68
69
64
69
68
70
70
70
63
64
66
71
72
66
64
73
73
74
64
65
70
75
76
77
65
69
66
68
64
77
66
76
69
Name:____________________
1. Graph the scatterplot of the data in the table to the left, where x
represents the height of the father and y represents the height of the
woman (the daughter).
2. Describe how the variables height of father and height of woman are
related.
3. Estimate the line of best fit for the data points on the scatterplot and graph this line.
4. Find the equation of your line of best fit.
5. Interpret the slope of your best fit line in context.
6. Interpret the y-intercept of your best fit line in context.
Scatterplots Level 2
Height of
Father (in)
62
63
Height of
Woman (in)
60
60
65
65
66
60
63
65
66
67
68
66
61
63
68
68
69
64
69
68
70
70
70
63
64
66
71
72
66
64
73
73
74
64
65
70
75
76
77
65
69
66
68
64
77
66
76
69
Name:____________________
1. Sketch a scatterplot of the data in the table to the left, where x
represents the height of the father and y represents the height of
the woman (the daughter).
2. Describe how the variables height of father and height of woman
are related.
3. Estimate the line of best fit for the data points on the scatterplot and graph this line.
4. Find the equation of your line of best fit.
5. Interpret the slope of your best fit line in context.
6. Interpret the y-intercept of your best fit line in context.
Scatterplots Level 3 (AP)
Name:_________________
Each of 25 adult women was asked to provide her own height (y), in inches, and the height (x), in inches, of
her father. The scatterplot below displays the result. Only 22 of the 25 pairs are distinguishable because
some of the (x,y) pairs were th same. The equation of the least squares regression line is yˆ  35.1  0.427 x .
a) Draw the least squares regression line on the scatterplot above.
b) One father’s height was x = 67 inches and his daughter’s height was y = 61 inches. Circle the point on
the scatterplot above that represents this pair and draw the segment on the scatterplot that
corresponds to the residual for it. Give a numerical value for the residual.
c) Suppose the point x = 84, y = 71 is added to the data set. Would the slope of the least squares
regression line increase, decrease or remain about the same? Explain. (Note: No calculations are
necessary to answer this question.)
Would the correlation increase, decrease or remain about the same?
Source: http://apcentral.collegeboard.com/apc/public/repository/ap07_stat_formb_frq_kw.pdf
http://apcentral.collegeboard.com/apc/public/repository/ap07_statistics_form_b_sgs_complete.pdf
Scoring Guidelines from AP:
Solution:
Parts (a) and (b): Draw the line and Find the Residual
When x = 67 the predicted height of the woman is 35.1  0.427(67)  63.709 .
The residual is the actual y value when x = 67 minus the predicted y-value when x = 67 or
y  yˆ  61  63.709  2.709 .
Parts (c): Effect of new points
See the new point indicated in the plot above. The slope would remain about the same since the new
point is consistent with the linear pattern in the original plot (i.e., close to the line).
The correlation coefficient would increase. We know that
br
sy
sx
. The added point would increase
the standard deviation in x more than it would in y so the ratios of standard deviations will be less
than 1. If the slope remains the same then r must increase.