Ten college students were randomly selected. Their grade point averages (GPAs) when they entered the program were between 3.5 and 4.0. The students' GPAs on entering the program (x) and their current GPAs (y) were recorded. The regression analysis is given below. Use the analysis to find a 95% confidence interval for the true slope.

The regression equation is y=3.584756+0.090953x with R-sq=0.001849 and 10-2=8 degrees of freedom

The regression equation is

ModifyingAbove y with caret

equals3.584756plus

0.090953x,

with

R-sqequals

0.001849,

and

10minus

2equals

8

degrees of freedom.

Predictor

Coeff

SE(Coeff)

T

P

Constant

3.584756

0.078183

45.85075

5.66x10-11

Entering GPA

0.090953

0.022162

4.103932

0.003419

The 95% confidence interval for the true slope is (0.03985, 0.14206).

Step-by-step explanation:

For the regression equation:

The (1 - α)% confidence interval for the regression coefficient or slope is:

The regression equation for current GPA (Y) of students based on their GPA's when entering the program (X) is:

The summary of the regression analysis is:

Predictor          Coefficient             SE             t-stat            p-value

Constant             3.584756          0.078183       45.85075      5.66 x 10⁻¹¹

Entering GPA   0.090953          0.022162        4.103932       0.003419

The regression coefficient and standard error are:

The critical value of t  for 95% confidence level and 8 degrees of freedom is:

Compute the 95% confidence interval for as follows:

Thus, the 95% confidence interval for the true slope is (0.03985, 0.14206).

yx = 36

step-by-step explanation:

cos f = opposite side/ hypotenuse

cos f = yw / yx

we know cos f = 4/9 and yw =16

4/9 = 16/yx

multiply each side by yx

4/9 yx = 16/ yx * yx

4/9 yx = 16

multiply each side by 9/4

9/4 * 4/9 yx = 16 *9/4

yx = 36