Mathematics, 28.12.2019 03:31 MaeWolfe

Using the same data, complete the following
a) perform a linear regression analysis with height the independent variable and weight the dependent, i. e.
weight=β₀+β₁×height+∈
• what is the prediction line equation?
• what is the r² value for this regression?
• what is the f-statistic value for testing the regressions significance?
b) test the hypotheses
h₀: β₁ = 0 vs $h_a$ : β₁ ≠ 0.
• what is the standard error of b₁?
• what is the test statistic value for this hypothesis test?
• what is the p-value for this test statistic?
• do you reject h₀?

Answers: 3

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Answers

Answer from: hi105

a) $weight = 49.995 +0.103height +\epsilon$

R^2 = 0.67051225196413

$R^2_{adj} =0.66160717769289$

F =75.2955260721013

b) H0: $\beta_1 =0$

H1: $\beta_1 \neq 0$

On this case the test statistc is given by t=8.67729946884982

And the p value obtined was: $p_v =1.88977483236692x10^{-10}$ and since the p value is lower than th significance level we can reject the null hypothesis at 5% of significance. The slope is significant.

$SE_{\beta_1}=0.0118255634597743$

Step-by-step explanation:

We assume the following info:

GenderHeightWeight

Male73.84701702241.8935632

Male68.78190405162.3104725

Male74.11010539212.7408556

Male71.7309784220.0424703

Male69.88179586206.3498006

Male67.25301569152.2121558

Male68.78508125183.9278886

Male68.34851551167.9711105

Male67.01894966175.9294404

Male63.45649398156.3996764

Male71.19538228186.6049256

Male71.64080512213.7411695

Male64.76632913167.1274611

Male69.2830701189.4461814

Male69.24373223186.434168

Male67.6456197172.1869301

Male72.41831663196.0285063

Male63.97432572172.8834702

Male69.6400599185.9839576

Male67.93600485182.426648

Male67.91505019174.1159291

Male69.43943987197.7314216

Male66.14913196149.173566

Male75.20597361228.7617806

Male67.89319634162.0066518

Male68.1440328192.3439766

Male69.08963143184.4351744

Male72.80084352206.8281894

Male67.42124228175.2139224

Male68.49641536154.3426389

Male68.61811055187.5068432

Male74.03380762212.9102253

Male71.52821604195.0322432

Male69.1801611205.1836213

Male69.57720237204.1641255

Male70.4009288 192.9035151

Male69.07617117197.4882426

Male67.19352328183.8109732

Male65.80731565163.8518249

And we can use excel to solve the problem

Part a

On this case we need to click on Data>Data analysis>Regression>Ok

We select the input Y range and th X range and then we click in Ok.

The output obtained is on the first figure attached.

And in order to estimate the regression line we need to look into the column Coefficients, and for this case we got:

$\beta_0 =49.995$

$\beta_1 =0.103$

And the linear model would be given by:

$weight = 49.995 +0.103height +\epsilon$

For the determination coefficient we have:

R^2 = 0.67051225196413

And the adjusted R^2 =0.66160717769289

And if we analyze the output th F statistic is given by:

F =75.2955260721013

Part b

We want to test:

H0: $\beta_1 =0$

H1: $\beta_1 \neq 0$

On this case the test statistc is given by t=8.67729946884982

The standard error for the slope is given in the output:

$SE_{\beta_1}=0.0118255634597743$

t=8.67729946884982

$p_v =1.88977483236692x10^{-10}$

We reject the null hypothesis.

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Using the same data, complete the following
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