Mathematics, 20.12.2019 20:31 KekePonds1021

Aresearcher gathers data on the length of essays (number of lines) and the sat scores received for a sample of students enrolled at his university. based on his regression results, the 95% confidence interval for the slope of the regression equation is minus−0.88 to 1.34. at alphaαequals=0.05, which of the following statements is true? (a) there is a statistically significant association between length of essays and sat score.(b) the relationship between length of essays and sat scores is significant and negative.(c) the slope of the regression equation is not significantly different from zero.(d) the slope of the regression equation is significantly different from zero.

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Answer from: mizu36011

Step-by-step explanation:

Let's suppose that we have the following linear model:

$y= \beta_o +\beta_1 X$

Where Y is the dependent variable and X the independent variable. $\beta_0$ represent the intercept and $\beta_1$ the slope.

In order to estimate the coefficients $\beta_0 ,\beta_1$ we can use least squares estimation.

If we are interested in analyze if we have a significant relationship between the dependent and the independent variable we can use the following system of hypothesis:

Null Hypothesis: $\beta_1 = 0$

Alternative hypothesis: $\beta_1 \neq 0$

Or in other wouds we want to check is our slope is significant.

In order to conduct this test we are assuming the following conditions:

a) We have linear relationship between Y and X

b) We have the same probability distribution for the variable Y with the same deviation for each value of the independent variable

c) We assume that the Y values are independent and the distribution of Y is normal

The significance level is provided and on this case is $\alpha=0.05$

The standard error for the slope is given by this formula:

$SE_{\beta_1}=\frac{\sqrt{\frac{\sum (y_i -\hat y_i)^2}{n-2}}}{\sqrt{\sum (X_i -\bar X)^2}}$

Th degrees of freedom for a linear regression is given by df=n-2 since we need to estimate the value for the slope and the intercept.

In order to test the hypothesis the statistic is given by:

$t=\frac{\hat \beta_1}{SE_{\beta_1}}$

The confidence interval for the slope would be given by this formula:

$\hat \beta_1 + t_{n-2, \alpha/2} \frac{\sqrt{\frac{\sum (y_i -\hat y_i)^2}{n-2}}}{\sqrt{\sum (X_i -\bar X)^2}}$

And using the last formula we got that the confidence interval for the slope coefficient is given by:

$-0.88 < \beta_1$

IF we analyze the confidence interval contains the value 0. So we can conclude that we don't have a significant effect of the slope on this case at 5% of significance. And the best option would be:

Answer from: Quest

The 3rd quadrant as 3x+g5ti=56i: 92d-543
What graph represents the system of linear inequalities? 3x+y> 1 y

Answer from: Quest

The answer would be b ! explanation: the formula for sa *surface area * is 2×l×w+2×l×h+2×w×h so in this case l=4w=12h=8so you use the formula to solve it and it give you the answer of 352^cm^2
Someone me. it would be nice if u could also explain how u ot the answer and how u do the equation

Someone me. it would be nice if u could also explain how u ot the answer and how u do the equation

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