Question

Some students in a school were surveyed to determine how many hours they study per night and their grade-point averages. The results are shown in the table. Hours Studying per Night vs. Grade-Point Average Hours studying per night, x Grade-point average, y 0.4 2.0 0.9 2.4 1.5 2.6 2.2 3.1 2.6 3.5 3.3 3.8 If the data are entered into a regression calculator, what is the approximate y-intercept of the resulting regression line?

Answer 1

Answer:

1.75927

Step-by-step explanation:

Refer the attached figure

x                  y                  

0.4               2

0.9               2.4

1.5                2.6

2.2               3.1

2.6               3.5

3.3                3.8

Mean = $\frac{\text{Sum of all observations}}{\text{Total no. of observations}}$

Mean of x values : $\frac{0.4+0.9+1.5+2.2+2.6+3.3}{6}= 1.8167$

Mean of y values : $\frac{2+2.4+2.6+3.1+3.5+3.8}{6}= 2.9$

$X-M_x$

-1.4167

-0.9167

-0.3167

0.3833

0.7833

1.4833

$Y-M_y$

-0.9

-0.5

-0.3

0.2

0.6

0.9

$(X-M_x)^2$

2.0069

0.8403

0.1003

0.1469

0.6136

2.2003

SS: 5.9083

$(X-M_x)(Y-M_y)$

1.275

0.4583

0.095

0.0767

0.47

1.335  

SP: 3.71

Sum of X = 10.9

Sum of Y = 17.4

Mean X = 1.8167

Mean Y = 2.9

Sum of squares (SS) = 5.9083

Sum of products (SP) = 3.71

Regression Equation = ŷ = bX + a

b = SP/SS = 3.71/5.91 = 0.62793

a =$M_y-bM_x$ = 2.9 - (0.63*1.82) = 1.75927

Thus ŷ = 0.62793X + 1.75927

Equation of line : y =mx+c

Where m = slope

c = y-intercept

Comparing regression equation with equation of line

ŷ = 0.62793X + 1.75927

m= 0.62793

y-intercept =1.75927

Hence the approximate y-intercept of the resulting regression line is 1.75927

Answer 2

1.76, this is the answer according to e2020/ingenuity <span />