the text appears to be free of spelling typographical grammatical ocr and mathematical errors 71

Name: the text appears to be free of spelling typographical grammatical ocr and mathematical errors 71578
Uploaded: 2023-04-28T19:42:25-08:00
Duration: 2 min 8 s
Channel: Ana Carolina Da Cruz
Description: the text appears to be free of spelling typographical grammatical ocr and mathematical errors 71578

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Regression analysis was performed using data for 24 single-family homes to predict appraised value (in thousands of dollars) based on land area of the property (in acres) X1 and age (in years) X2. In this analysis, the following results were obtained: Standard Variable Coefficient Standard Error t-statistic p-value Intercept 402.05762 50.10394 8.02 0.0000 Area, X1 451.31807 114.46072 3.94 0.0007 Age, X2 2.19371 0.61574 3.56 0.0018 At the 0.05 level of significance, we need to determine whether each independent variable makes a significant contribution to the regression model. Based on these results, we can determine which independent variables should be included in the model.

Ana Carolina D.

A real estate agency collects the data concerning • y = sales price of a house (in thousands of dollars) • x1 = home size (in hundreds of square feet) • x2 = rating (an overall “niceness rating” for the house expressed on a scale from 1 [worst] to 10 [best], and provided by the real estate agency) The agency wishes to develop a regression model that can be used to predict the sales prices of future houses it will list. X1 X2 Y Home Size Rating Sales Price 23 5 180.0 11 2 98.1 20 9 173.1 17 3 136.5 15 8 141.0 21 4 165.9 24 7 193.5 13 6 127.8 19 7 163.5 25 2 172.5 a) Interpret the equation parameters b0, b1, and b2 b) Interpret R 2 and R̄ 2 . Show how R̄ 2 has been calculated from R 2 and other relevant quantities. c. Overall Test of the Model • Write the hypothesis statement to test the significance of the overall regression relationship or that your model is effective. • Calculate the F(model) statistic by using the explained and unexplained variations (as shown on the output) and other relevant quantities. Find F(model) on the output to check your answer (within rounding). • Use the F(model) statistic and the appropriate critical value (from the F-table) to test your hypothesis by setting α equal to .05. • Find the p-value related to F(model) on the output. Using the p-value, test the significance of the linear regression model by setting α =.05. • What do you conclude? d. Testing the Significance of Independent Variables • For every parameter use the t statistic and appropriate critical values (from t-table) to test the significance of the independent variable xj by setting α equal to .05: H0: βj = 0 versus Ha: βj ≠ 0 • Which independent variables are significantly related to y at α = .05? • For every parameter find the p-value for testing H0: βj = 0 versus Ha: βj ≠ 0 on the output. Using the p-value, determine whether we can reject H0 by setting α equal to .05. • What do you conclude about the significance of the independent variables in the model?

Sri K.

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Fifty children from each of two neighborhoods are given identical reading tests. The researcher is primarily interested in whether children in the two neighborhoods score significantly differently from each other. The researcher is also interested in how a child's age plays into the relationship between neighborhood and reading score. A regression was run with the variables defined as: Y, reading score; Xage, age in years and months; Xnbd, which is zero for children from neighborhood A and one for children from neighborhood B. The following are the standard regression output and the sequential Sum of Squares table for the regression: The model was: Y = β0 + β1 Xage + β2 Xnbd + β3 Xage:Xnbd + ε, where ε ~ N(0, σ^2). Coefficients: (Intercept) 16.457 12.985 1.267 0.208097 Xage 5.046 1.481 3.406 0.000964 Xnbd -36.304 18.812 -1.930 0.056584 Xage:Xnbd 4.521 2.192 2.062 0.041863 Residual standard error: 22.09 on 96 degrees of freedom Multiple R-squared: 0.3273, Adjusted R-squared: 0.3062 F-statistic: 15.57 on 3 and 96 DF, p-value: 2.508e-08 Sequential Sum of Squares Table (Response: y): Xage 1 20669 Xnbd 1 49 Xage:Xnbd 1 2076 Residuals 96 46858

Dominador T.

Transcript

00:01 So to answer this question, we should use the results from the table.

00:04 So for example, for the first part of this question, we are testing everything about x1.

00:09 X1 is the area.

00:10 So we should focus on the row related to x1.

00:14 So when we are testing if this variable is significant or not for our regression model, what we are testing is if the slope of the variable is either 0, which means that it can be removed from the model, or not.

00:27 So basically, that's what we have as hypothesis.

00:32 And in this case, the right option is letter a.

00:35 Beta 1 here represents the slope for the area, which is the coefficient x1.

00:42 Then the t statistic is the value in the row related to the test statistic.

00:50 So in this case, it's 394...

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