# STAT 154-If the Pearson’s correlation coefficient

1. If the Pearson’s correlation coefficient between two variables X and Y is found to benegative1.3. This meansWeak negative correlation between variables X and Y Strong negative correlation between variables X and Y Weak positive correlation between variables X and Y Correlation value is not possible Strong positive correlation between variables X and Y 2. To test the hypothesis that population correlation coefficient is not zero, wecollected a sample of size 15 and found the sample correlation coefficient is 0.25.What is the test value to test this hypothesis?1 0.25 0.93 0.75 1.53. Correlation is calculated using 20 pair of sample data. Find the degrees of freedomto test the hypothesis about correlation.Question 3 options: 18 20 25 19 21 4. Following table shows study hours per week and GPA of five students Study hrs 2 5 7 4 8 GPA 1.7 3.2 3.8 3.5 4.0 Calculate the Pearson’s correlation coefficient between Study hours and GPA ofthe students students.Question 4 options:0.79 0.59 0.89 0.62 0.99 5. Following table shows study hours per week and GPA of five students Study hrs 2 5 7 4 8 GPA 1.7 3.2 3.8 3.5 4.0 Calculate the test value to test the claim that there is significant correlation between Studyhours and GPA of the students.Question 5 options:3.38 2.75 4.21 1.28 2.12 6. Following table shows study hours per week and GPA of five students Study hrs 2 5 7 4 8 GPA 1.7 3.2 3.8 3.5 4.0 Calculate the p-value to test the claim that there is significant correlation between Study hoursand GPA of the students.Question 6 options:10% < p value < 20% 5% < p value < 10% 1% < p value < 2% 1% < p value < 2.5% 2% < p value < 5%7. Following table shows study hours per week and GPA of five students Study hrs 2 5 7 4 8 GPA 1.7 3.2 3.8 3.5 4.0 Calculate the p-value to test the claim that there is significant correlation between Studyhours and GPA of the students. If alpha is 5% what is your decision?Question 7 options:There is significant correlation between two variables. There is no significant correlation between two variables. Not enough information to make decision8. Following table shows study hours per week and GPA of five students Study hrs 2 5 7 4 8 GPA 1.7 3.2 3.8 3.5 4.0 Calculate the critical value to test the claim that there is significant correlation betweenStudy hours and GPA of the students. Take alpha is 5%.Question 8 options:2.571 2.353 3.182 2.0159. Use the following regression model for prediction:Beta0hat = 5.45, Beta1hat =-0.182. Find dependent variable Yhat when X is 2.5Note:Beta0hat = Estimate of Y interceptBeta1hat = Estimate of slope of the regression lineQuestion 9 options:2.99 9.99 4.99 6.99 2.3910.In simple linear regression modelY = ?0+ ?1X +?what is ? ? Question 10 options:Variance of the model Predictor Variable Random error Response variable Parameter to be estimated 11. In simple linear regression model Y = ?0+ ?1X +?what is Y ? Question 11 options:Predictor Variable Variance of the model Random error Response variable Parameter to be estimated12. Table below gives the weight of diamond and price in dollars.Which one is the response variable? Weight Price 0.3 510 0.4 1151 0.5 1343 0.5 1410 1.0 5669 0.7 2277 Question 12 options:Price Weight Both Weight and Price We can not say which one from the given information 13. Table below gives the weight of diamond and price in dollars.Fit a simple linear regression model to find what is the estimate of intercept parameter ?(due to rounding error go to the closest answer) Weight Price 0.3 510 0.4 1151 0.5 1343 0.5 1410 1.0 5669 0.7 2277 Question 13 options:7177 1278 -7177 -200714. Table below gives the weight of diamond and price in dollars.Fit a simple linear regression model to find what is the estimate of the slope parameter ?(due to rounding error go to the closest answer) Weight Price 0.3 510 0.4 1151 0.5 1343 0.5 1410 1.0 5669 0.7 2277 Question 14 options:7177 -7177 1278 -200715. Table below gives the weight of diamond and price in dollars.Fit a simple linear regression model and estimate the price if the weight of the diamond is1.5 carats ? (due to rounding error go to the closest answer) Weight Price 0.3 510 0.4 1151 0.5 1343 0.5 1410 1.0 5669 0.7 2277 Question 15 options:1278 7177 2834 875916. If pair of 10 observations show the correlation coefficient 0.37. To test thesignificance of the population correlation coefficient find test valueQuestion 16 options:1.32 3.10 1.13 2.56 2.90 17. Suppose the population correlation coefficient between two variables X and Y iso.77 , covariance of X and Y is 2.7 and standard deviation of X is 1.5. Find thestandard deviation of Y.Question 17 options:5.46 0.92 1.42 3.12 2.3418. Calculate correlation between X and Y from 6 pairs of observations If we knowSum of XY =20485Sum of X= 247Sum of Y= 486Sum of X square= 11409Sum of Y square= 40022 Question 18 options:0.19 0.95 0.23 0.71 0.53 19. When testing the hypothesis about parameters of multiple linear regression modelH0: B1=B2=….=Bk=0H1: at least one Bi is not zero.we useQuestion 19 options:F test t test Z-test chi-square test20. Which of the following is not the assumption of a linear regression model?Question 20 options:Errors are independent Error term has the same variance in eachobservation. Response variable (Y) and predictors (X) are linearly related. Error term is normally distributed Values of the response variable (Y) must be categorical(Bonus) 21. Table below gives the systolic blood pressure measurement in left and rightarm.Estimate the blood pressure in left arm given that blood pressure in right arm is 135 mmHg. Right Arm Left Arm 102 175 101 169 94 182 79 146 79 144 Question 21 options:198.07 312.17 120.25 256.18 221.1221.