QUESTION 1 Answer (a): According to this problem, the p value is very small for the F test. Hence, the null hypothesis needs to be rejected (Conclusion). This basically means that at least 1 of the predictor variables seems to have a linear relationship with the outcome variable. We don’t know which outcome variable it is. The null hypothesis for this F test says that all slopes of each and every predictor variable in the regression model equal to 0 – this basically means that each of the predictor variable has no linear relationship with the outcome variable. Answer (b): The t tests tell us if the predictor variable has a significant linear association with the outcome variable or not. The alpha value of 0.05 is used; if the value of …show more content…
In Model 2, we can see that it has a better F test but it’s RSE and adjusted R2 value is the same. The regular R2 value and the adjusted R2 value is different because it depends on the number of variables we have in our model. As we know, an R2 value closer to 1 means that the values are good – but that isn’t the case here. Here, the R2 value will definitely increase with an increase in the number of variables, but that does not qualify for the variables to be good (more model parameters better fit, higher R2). Adjusted R2 formula punishes us for having many numbers (i.e. if we have added more numbers unnecessarily). It shows us the variation in y axis and level of efficiency (with regard to using less variables). Answer (d): The slope in Model 2 (multiple linear regression) shows us the consequences of changing a unit on y axis, while keeping all the x variables constant. For example, if the weight is increased by 1 point, the pemax also increases by 1.64. The bmp remains constant. If the bmp is increased by 1 point, the pemax decreases by 1.005 (weight remains constant). Answer (e): I think that Models 3 and 4 are in consistent with Model 2. According to me, the difference lies in the way we interpret them. There is only 1 variable in Model 3 as well as in Model 4, hence, the interpreted answer misses out on the control of the other variable. Model 3 shows us the consequence of
6. Although you are basically satisfied with the analysis thus far, you are concerned about the
Assignment 4: I developed a hypothesis to predict what effect an increase in island size will have on beak size and finch populations. I tested my hypothesis by leaving all other parameters at their default values. Selected the Island Size input and use the sliders to increase the size of either. Then I tested the effect of the parameters to influence population size and beak size by designing and running experiments to get my
4. Based on your analysis in (1) – (3) above, what is your overall conclusion regarding the
Exercises 12.17, 12.21, and 12.43 require the use of the “Regression” function within the Data Analysis menu in Excel. Refer to Appendix E12 for instructions on using Excel for these exercises.
b. Dependent Variable: the variable that I am measuring (it depends on the independent variable)
22) Which statement is true of a regression line that is superimposed on the scatter plot?
Slide 17: This curve demonstrates a one-tail hypothesis with the critical region representing 5% showing a negative relationship.
Reporting t values- when you have already reported p values- is not necessary and can cause confusion.
Table 6.1.1 displays the matlab output of beta, standard error, t-statistic and p-value for the two independent variables during 10-year period. It is found that beta of X1 is 0.2750 which indicates there is a positive relationship between the utilities excess return and the healthcare excess return. This positive relationship is statistically significant as the p-value is close to 0 which is much less than the significance level of 5%. In addition, the standard error of X1 is 0.0300 which represents the average distance that the observed values fall from the regression line. This indicates that the model fits the data. In contrast, it is found that the material excess return is negatively
It tells that the t-statistic with 97 degrees of freedom was 2.14, and the corresponding p-value was less than .05, specifically around 0.035. Therefore, it is appropriate to conclude the research study was statistically significant.
For this independent t test, the mean GPAs of 64 females and 41 males were compared. The variables used are (1) gender, and (2) GPA. The predictor, or independent, variable is gender. And the outcome variable is GPA. Gender can only have two values, male or female; this
s squared subscript p=(n1-1)s squared2 subscript1+(n2-1)s squared2 subscript2]/n1+n2-2. The numerator of the function, n1+n2-2, is the degrees of freedom.
Your task is to determine which of the three major causal models (i.e., interpretations) could account for each finding. Indicate in the table below, by placing an X in the appropriate space, which of these three models could provide a possible explanation. Place an X in the space only if you judge the causal model to be possible & reasonably plausible. If you decide that the third model is possible, generate two possibilities for what variable “C” could represent, and type a short summary (one to 4 words should be sufficient) of these variables in
Run the regression Report your answer in the format of equation 5.8 (Chapter 5, p. 152) in the textbook including and the standard error of the regression (SER). Interpret the estimated slope parameter for LOT. In the interpretation, please note that PRICE is measured in thousands of dollars and LOT is measured in acres.
Heteroskedasticity test is also done for the model I and the results look like seen below in Table 5.12. Since the Obs*R2 value of 8.092 is less than the 5% critical X2 value of 11.07, the null hypothesis that assumes unavailability of heteroskedasticity can’t be rejected. That implies that the standard errors, T-statistics and F-statistics can be considered valid.