Question

In: Statistics and Probability

Question: Compute F and use it to test whether the overall model is significant using a...

Question: Compute F and use it to test whether the overall model is significant using a p-value (α = 0.05).

The estimated regression equation for a model involving two independent variables and 65 observations is:

yhat = 55.17+1.1X₁ -0.153X₂

Other statistics produced for analysis include: SSR = 12370.8, SST = 35963.0, S_b1 = 0.33, S_b2 = 0.20.

Expert Solution

The model being estimated is

where is the intercept

are the slope coefficients for

is a random disturbance

to test whether the overall model is significant, the hypotheses are

n=65 is the number of observations

k=2 is the number of independent variables

The sum of square regression (SSR) is

The degrees of freedom for SSR = k=2

The sum of square total is

The sum of square errors is

The degrees of freedom for SSE = n-k-1=65-2-1=62

The F statistics is

ans: F statistics is 16.26

The numerator degrees of freedom =2 and the denominator df=62

The using the F table for alpha=0.05 and numerator degrees of freedom =2 and the denominator df=60 (the closest to 62), we get a critical value of 3.15.

We will reject the null hypothesis if the test statistics is greater than the critical value for alpha=0.05.

Here, the test statistics is 16.26 and it is greater than the critical value 3.15. Hence we reject the null hypothesis.

ans: We conclude that there is sufficient evidence to support the claim that the overall model is significant.

orchestra answered 1 year ago

Is your overall model significant? Provide statistical proof by conducting an F-test for overall fit of the regression

SALARY EDUC EXPER TIME 39000 12 0 1 40200 10 44 7 42900 12 5 30 43800 8 6 7 43800 8 8 6 43800 12 0 7 43800 12 0 10 43800 12 5 6 44400 15 75 2 45000 8 52 3 45000 12 8 19 46200 12 52 3 48000 8 70 20 48000 12 6 23 48000 12 11 12 48000 12 11 17 48000 12 63 22 48000 12 144 24 48000 12 163...

Use t and F to test for a significant relationship between HRS1 and age. Use α...

Use t and F to test for a significant relationship between HRS1 and age. Use α = 0.05 and make sure you know what hypotheses you are using to conduct the significance tests. Calculate and interpret the coefficient of determination R2. Based on this R2, did the estimated regression equation provide a good fit? Briefly justify your answer. Hint: If you used Excel Regression Tool to answer part c, R2 was reported with your output. Use the estimated regression equation...

Using this model: propose a single model with which you can test whether: (a) the relationship...

Using this model: propose a single model with which you can test whether: (a) the relationship between population(POP) and CO2 emissions is nonlinear and quadratic; (b) the relationship between income(GNI) and CO2 emissions is nonlinear and quadratic; (c) the impacts of population and income(GNI) on CO2 emissions are different in different years; and (d) the impact of population(POP) on CO2 emissions is different at higher than at lower income levels. What does your model look like? (Hint: You will have...

Find a function f such that F = ∇f and use it to compute R C...

Find a function f such that F = ∇f and use it to compute R C Fdr along curve C. • F = <x, y>, C is part of the parabola y = x ^ 2 from (−1, 1) to (3, 9). • F = <4xe ^ z, cos (y), 2x ^ 2e ^ z>, where C is parameterized by r (t) = <t, t ^ 2, t ^ 4>, 0 ≤ t ≤ 1.

In a simple linear regression model, the ANOVA F test is a test of model significance...

In a simple linear regression model, the ANOVA F test is a test of model significance (i.e. a test of whether the linear regression model is significantly better than the trivial model yi = β0 + εi). This test can be performed in another way (i.e. by the 'extra sum of squares' or ESS method considering the simple linear regression model as the 'full model' and the trivial model yi = β0 + εi as the 'reduced model'). There is...

Use the Wilcoxon matched-pairs signed rank test to determine whether there is a significant difference between...

Use the Wilcoxon matched-pairs signed rank test to determine whether there is a significant difference between the related populations represented by the data below. Assume a 5% level of significance and (differences = before - after). Before After 5.6 6.4 1.3 1.5 4.7 4.6 3.8 4.3 2.4 2.1 5.5 6.0 5.1 5.2 4.6 4.5 3.7 4.5 What is the value of T-? What is the value of T+? What is the test statistic, T? Using the table of Critical Values, what is the critical value for this study?

Using the following data (already sorted), use a goodness of fit test to test whether it...

Using the following data (already sorted), use a goodness of fit test to test whether it comes from an exponential distribution. The exponential distribution has one parameter, its mean, μ (which is also its standard deviation). The exponential distribution is a continuous distribution that takes on only positive values in the interval (0,∞). Probabilities for the exponential distribution can be found based on the following probability expression: . Use 10 equally likely cells for your goodness of fit test. Data...

Question 1: You are evaluating whether the use of red lights during evaluation has a significant...

Question 1: You are evaluating whether the use of red lights during evaluation has a significant effect on liking. Liking was measured as either like or dislike. You collected the below data. Using the Sign Test, did the wine glass significantly influence liking? There is a worked example using the sign test (5 pts) Panelist Liking of wine: No red light Liking of wine: With Red light Direction of change 1 Like Like 2 Dislike Like 3 Dislike Like 4...

Use the appropriate test to determine whether X1 can be dropped from the regression model given...

Use the appropriate test to determine whether X1 can be dropped from the regression model given that X2 is retained. Use level of significance 0.05. Find the value of appropriate test statistic, the critical vale and the P-value. Plese show me how to use R to solve this. 0.1537; 4.6679; 0.7014 0.1537; 4.3245; 0.6523 1.537; 4.6932; 0.4128 2.5632; 4.6679; 0.3128 X1 X2 Y 190 130 35 176 174 81.7 205 134 42.5 210 191 98.3 230 165 52.7 192 194 ...

Use an independent-measures t test with α = .05 to determine whether there is a significant mean difference between the two treatments.

N =16 G = 120 ΣX² = 1036 The following scores are from an independent-measure study comparing two treatment conditions. Treatment I II 10 7 8 4 7 9 9 3 13 7 7 6 6 10 12 2 Use an independent-measures t test with α = .05 to determine whether there is a significant mean difference between the two treatments. Use an ANOVA with α = .05 to determine whether there is a significant mean difference between the...