$\"\"$

The winning heights for the men $\"\"$ s Olympic pole vault competitions are observed in

the table up to the year $\"\"$ .

Consider the years as $\"\"$ and men $\"\"$ s height as $\"\"$ .

(a)

(1) Draw the coordinate plane.

(2) $\"\"$ axis: Years as $\"\"$ .

(3) $\"\"$ axis: men $\"\"$ s height as $\"\"$ .

(4) Plot the data of values in the plane.

$\"\"$

Observe the graph:

The linear model is appropriate.

$\"\"$

(b)

Regression line:

The process of data points and coming up with an equation is called regression,

and the graph of the regression equation is called regression line.

The equation for linear regression is $\"\"$ .

Where $\"\"$ and $\"\"$ .

Now calculate the values for $\"\"$ and $\"\"$ .

The winning heights for the men $\"\"$ s Olympic pole vault competitions

can be tabulated as shown below:

In below table the starting year treated as $\"\"$ .

\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \

S.no	Years $\"\"$	Height $\"\"$	$\"\"$	$\"\"$	$\"\"$
1	1896 $\"\"$	$\"\"$	0	0	10.89
2	1900 $\"\"$	$\"\"$	13.2	16	10.89
3	1904 $\"\"$	$\"\"$	28	64	12.25
4	1908 $\"\"$	$\"\"$	44.52	144	13.76
5	1912 $\"\"$	$\"\"$	63.2	256	15.60
6	1920 $\"\"$	$\"\"$	98.16	576	16.72
7	1924 $\"\"$	$\"\"$	110.6	784	15.60
8	1928 $\"\"$	$\"\"$	134.4	1024	17.64
9	1932 $\"\"$	$\"\"$	155.16	1296	18.57
10	1936 $\"\"$	$\"\"$	174	1600	18.92
11	1948 $\"\"$	$\"\"$	223.6	2704	18.49
12	1952 $\"\"$	$\"\"$	254.8	3136	20.70
13	1956 $\"\"$	$\"\"$	273.6	3600	20.79
14	1960 $\"\"$	$\"\"$	300.8	4096	22.09
15	1964 $\"\"$	$\"\"$	346.8	4624	26.01
16	1968 $\"\"$	$\"\"$	388.8	5184	29.16
17	1972 $\"\"$	$\"\"$	428.64	5776	31.80
18	1976 $\"\"$	$\"\"$	451.2	6400	31.80
19	1980 $\"\"$	$\"\"$	485.52	7056	33.40
20	1984 $\"\"$	$\"\"$	506	7744	33.06
21	1988 $\"\"$	$\"\"$	542.8	8464	34.81
22	1992 $\"\"$	$\"\"$	563.52	9216	34.45
23	1996 $\"\"$	$\"\"$	592	10000	35.04
24	2000 $\"\"$	$\"\"$	613.6	10816	34.81
25	2004 $\"\"$	$\"\"$	642.6	11664	35.40
$\"\"$	1400	129.32	7435.52	106240	592.65

Observe the table:

$\"\"$ , $\"\"$ , $\"\"$ , $\"\"$ , $\"\"$ .

The number of samples are $\"\"$ .

$\"\"$