Find the estimated slope and y-intercept. Round to 3 decimal places. Determine t

Question

Find the estimated slope and y-intercept. Round to 3 decimal places.

Determine the value of the dependent variable y^ (y hat) at x = 0

Find the estimated value of y when x = 64. Round to 3 decimal places.

Substitute the values you found in steps 1 and 2 into the equation for the regression line to find the estimated linear model. According to this model, if the value of the independent variable is increased by one unit, then find the change in the dependent variable y hat

Find the value of the coefficient of determination. Round to 3 decimal places.

The table below gives the age and bone density for five randomly selected women. Using this data, consider the equation of the regression line, y = bo + bix, for predicting a woman's bone density based on her age. Keep in mind, the correlation coefficient may or may not be statistically significant for the data given. Remember, in practice, it would not be appropriate to use the regression line to make a prediction if the correlation coefficient is not statistically significant. Age 3943 466164 Bone Density 352 346 321 314 312

Explanation / Answer

Result:

Find the estimated slope and y-intercept. Round to 3 decimal places.

Regression Analysis

r²

0.789

n

5

r

-0.888

k

1

Std. Error

9.909

Dep. Var.

Bone density

ANOVA table

Source

SS

df

MS

F

p-value

Regression

1,101.4545

1  

1,101.4545

11.22

.0441

Residual

294.5455

3  

98.1818

Total

1,396.0000

4  

Regression output

confidence interval

variables

coefficients

std. error

   t (df=3)

p-value

95% lower

95% upper

Intercept

404.0116

22.8297

17.697

.0004

331.3573

476.6658

age

-1.4824

0.4426

-3.349

.0441

-2.8910

-0.0739

Slope= -1.482

Intercept=404.012

Determine the value of the dependent variable y^ (y hat) at x = 0

The regression line is Bone density =404.012-1.482*age

When age =0, bone density =404.012.

Find the estimated value of y when x = 64. Round to 3 decimal places.

when x = 64, estimated Bone density =404.012-1.482*64

=309.164

Substitute the values you found in steps 1 and 2 into the equation for the regression line to find the estimated linear model.

According to this model, if the value of the independent variable is increased by one unit, then find the change in the dependent variable y hat by 1.482

Find the value of the coefficient of determination. Round to 3 decimal places.

coefficient of determination=0.789

Regression Analysis

r²

0.789

n

5

r

-0.888

k

1

Std. Error

9.909

Dep. Var.

Bone density

ANOVA table

Source

SS

df

MS

F

p-value

Regression

1,101.4545

1  

1,101.4545

11.22

.0441

Residual

294.5455

3  

98.1818

Total

1,396.0000

4  

Regression output

confidence interval

variables

coefficients

std. error

   t (df=3)

p-value

95% lower

95% upper

Intercept

404.0116

22.8297

17.697

.0004

331.3573

476.6658

age

-1.4824

0.4426

-3.349

.0441

-2.8910

-0.0739

Related Questions

Navigate

• Browse (All)
• Browse F
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.