You have a multiple regression that contains one dependent variable Y and four independent variables X1, X2, X3 and X4 with population coefficients β1, β2, β3 and β4.  What is the F-test used for?   a. To test the null hypothesis that all the coefficients β1, β2, β3 and β4 are zero   b. To test the null hypothesis that β1 ≠ 0   c. To test the null hypotheses that only one of the coefficients is zero   d. To test the null hypothesis that β2 ≠ 0

3 of 14 For many people, the women's figure skating competition is the highlight of the Olympic Winter Games. Scores in the short program x and scores in the free skate y were recorded for each of the 24 skaters who competed in both rounds during the 2010 Winter Olympics in Vancouver, Canada. Here is a scatterplot with least-squares regression line y =-16.2 +2.07x. For this model, s = 10.2 and = 0.736. 160 Interpret the value of s. 140 O 10.2% of the variation in free skate score is 120 accounted for by the least-squares regression line with x = short program score. The actual free skate score is typically about 10.2 points lower than the score predicted by the least- squares regression line with x = short program score. O For every 1 point increase in the short program score, the predicted free skate score increases by 10.2 points. O The actual free skate score is typically about 10.2 points higher than the score predicted by the least- squares regression line with x = short program…

A researcher would like to predict the dependent variable Y from the two independent variables X1 and X2 for a sample of N=15 subjects.  Use multiple linear regression to calculate the coefficient of multiple determination and test the significance of the overall regression model.  Use a significance level α=0.01. X1X1 X2X2 YY 44.5 64.2 39.3 27.4 58.2 18.8 37.6 74 40.2 40.5 12.1 73.3 33.4 60.8 15.5 0.3 21.7 27.4 91.4 57 69.8 56.4 58.9 98.4 30.8 46.8 40 54 83.2 31.5 31.6 66.2 29.8 37.5 57.1 46.7 55.3 38.7 99.8 66 61.2 84.1 53.7 37.9 45.9 SSreg=SSres=R2=F= P-value =

A researcher would like to predict the dependent variable Y from the two independent variables X1 and X2 for a sample of N = 12 subjects. Use multiple linear regression to calculate the coefficient of multiple determination and test statistics to assess the significance of the regression model and partial slopes. Use a significance level a = 0.01. X1 X2 53.2 50.8 61.2 91.9 84.6 66.8 62 57.8 61.9 46.4 43 70.1 59.1 65.5 56.5 72.6 61.7 62.7 69.5 70.4 63.7 70.9 70.6 64.9 68.6 61.5 61.1 54.7 57 49 34.6 43.9 45 67.2 This data set can be downloaded as a *.csv file: Download CSV. 41.6 44.4 R F = P-value for overall model = ti = for b1, P-value = tą = for b2, P-value = What is your conclusion for the overall regression model (also called the omnibus test)? O The overall regression model is statistically significant at a = 0.01. O The overall regression model is not statistically significant at a = 0.01. Which of the regression coefficients are statistically different from zero? O neither…

Suppose Wesley is a marine biologist who is interested in the relationship between the age and the size of male Dungeness crabs. Wesley collects data on 1,000 crabs and uses the data to develop the following least-squares regression line where ? is the age of the crab in months and ?ˆ is the predicted value of ?, the size of the male crab in cm. ?ˆ=8.1312+0.5226?   What is the value of ?ˆ when a male crab is 23.0736 months old? Provide your answer with precision to two decimal places. ?ˆ =     Interpret the value of ?. The value of ?ˆis the predicted size of a crab when it is 23.0736 months old. the predicted incremental increase in size for every increase in age by 23.0736 months. the predicted number of crabs out of the 1,000 crabs collected that will be 23.0736 months old. the probability that a crab will be 23.0736 months old.

The systolic blood pressure of individuals is thought to be related to both age and weight. For a random sample of 11 men, the following data were obtained. Systolic Blood pressuex1 Age (years)x2 Weight (pounds)x3 132 52 173 143 59 184 153 67 194 162 73 211 154 64 196 168 74 220 137 54 188 149 61 188 159 65 207 128 46 167 166 72 217   a) Look at the coefficients of the regression equation. Write out the regression equation. (Use 3 decimal places.) x1 = _____ + _____ x2 + ____x3   b) If age were held fixed, but a person put on 10 pounds, what would you expect for the corresponding change in systolic blood pressure? (Use 2 decimal places.)c) If a person kept the same weight but got 10 years older, what would you expect for the corresponding change in systolic blood pressure? (Use 2 decimal places.)

A researcher would like to predict the dependent variable YY from the two independent variables X1 and X2 for a sample of N=13 subjects.  Use multiple linear regression to calculate the coefficient of multiple determination and test statistics to assess the significance of the regression model and partial slopes.  Use a significance level α=0.01. X1 X2 Y 38.3 52.7 55.5 50.9 76 89.3 33.5 57.6 18.6 40.9 43.6 27.7 48.7 63.5 76.5 49.6 73.3 57.4 36.9 53.3 29.8 35.4 62.8 50.2 39 76.3 65.4 64.9 57.7 71.5 54.8 58 51.5 37.8 62.6 54.7 56.7 50.5 36.6 R2=F= P-value for overall model = t1=for b1, P-value = t2= for b2, P-value =

When is a variable in a regression statistically significant? 1   When p is more than alpha. 2   When p is more than R2. 3   When p is less than alpha. 4   When p is less than R2. 5   When p is less than the coefficient.

A researcher would like to predict the dependent variable YY from the two independent variables X1X1 and X2X2for a sample of N=20N=20 subjects.  Use multiple linear regression to calculate the coefficient of multiple determination and test the significance of the overall regression model.  Use a significance level α=0.02. X1X1 X2X2 YY 31.4 32.3 25.2 85.4 28.1 53 66.3 42.6 67.4 59 56.1 70.7 52.4 40.4 39.7 86.4 23.7 35 50.9 36.7 34.4 74.4 38 64.9 57.3 47.6 67.4 61.9 33.3 41.3 48.6 49.7 53.6 46.6 47.2 34.5 31.8 38.7 40.9 86 55 74 69.8 27.7 45.9 65.8 48.2 42.4 44.7 55.3 55.1 57.3 27 31.5 60.4 28.1 19.4 65.9 26 13.7 SSreg=  SSres=  R2=  F=  P-value = What is your decision for the hypothesis test? Reject the null hypothesis, H0:β1=β2=0 Fail to reject H0H0 What is your final conclusion? The evidence supports the claim that one or more of the regression coefficients is non-zero The evidence supports the claim that all of the regression…