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4 years ago

11

A random sample of 11 students produced the following data, where x is the hours spent per month playing games, and y is the fin

al exam score (out of a maximum of 50 points). The data are presented below in the table of values.
x y
14 46
15 49
16 37
17 42
18 37
19 31
20 25
21 23
22 20
23 15
24 12
What is the value of the intercept of the regression line, b, rounded to one decimal place?

1 answer:

Sholpan [36]4 years ago

4 0

Answer:

b = - 3.7

Step-by-step explanation:

here are the data values:

x y XY X²

14 46 644 196

15 49 735 225

16 37 592 256

17 42 714 289

18 37 666 324

19 31 589 361

20 25 500 400

21 23 483 441

22 20 440 484

23 15 345 529

24 12 288 576

now we are required to find the summation (total) of all values of X, Y, XY and X².

∑X = 209

∑Y = 337

∑XY = 5996

∑X² = 4081

The formular for finding b is given as:

b = n∑XY - (X)(Y) / n∑X² - (∑X)²

= 11(5996) - (209)(337) / 11(4081) - (209)²

= 65956 - 70433 / 44891 - 43681

= -4477/ 1210

= -3.7

The question asked us to find the <em>value of b</em> but we can go further to find the equation of the regression line:

a = ∑Y - b∑X / n

= 337 - (-3.7)(209)/ 11

=1110.3/11

= 100.94

the equation is:

Y = 100.94 - 3.7X

I hope you find my solution useful!

=

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