Math 146 - Introductory Statistics - Hybrid - Spring 2015
Quiz 7 (total points: 10)
June 10, 2015
Name: __________________________________
1. (2 pt) True or False.
a) A correlation coefficient can never be zero. False
b) Multiple regression involves more than one response variable for a given explanatory variable.
False
c) A coefficient of determination of 0.9 shows strong positive correlation. False
d) A golfer wants to determine if the number of lessons received every year can be used to predict the
amount of improvement in his game. The explanatory variable is the number of lessons. True
2. (1 pt) a) What does the sample correlation coefficient r measure?
The strength and direction of a linear relationship
b) Describe the range of values for the correlation coefficient.
−𝟏 ≤ 𝒓 ≤ 𝟏
3. (1 pt) Which value indicates a stronger correlation: r = 0.918 or r = -0.932? Explain your reasoning.
-0.932 because its absolute value is closer to 1 (or --- because it is farther from zero)
4. (1 pt) a) What is a residual? The difference between an observed data value and the
predicted data value using a regression line
b) Explain (in terms of data points and regression line) when a residual is zero.
The regression line goes through the data point (or the point is on the line …)
5. (1 pt) One wants to determine if there is a linear relationship between a country’s GDP and
carbon dioxide emissions. Ten data points are collected and a correlation coefficient has been
computed. Give the hypotheses one would use to test the significance of the correlation.
6. (1 pt) a) The correlation of the hours watching TV and GPA (n=7) data is r = -0.818. Given the
table below, is the correlation coefficient significant at the 0.05 significance level? Why or why not?
n
4
5
6
7
8
α = 0.05
0.950
0.878
0.811
0.754
0.707
α = 0.01
0.990
0.959
0.917
0.875
0.834
Yes because | -8.18 | > 0.754
b) Interpret your result.
At the 5% significance level there exists significant correlation between GDP and carbon dioxide
emissions.
7. (1 pt) In order to predict y-values using the equation of a regression line, what must be true about
the correlation coefficient of the variables?
It must be significant.
8. (1 pt) a) Use the value of the linear correlation coefficient to calculate the coefficient of
determination.
r = .9
r2 = .81
b) What does this tell you about the explained variation of the data about the regression line?
81% of the variation in the y values are explained by the linear relationship (or by the variation
in the x values)
9. (1 pt) a) The independent variable is length of glubs. The dependent variable of weight of glubs. If
the values for m and b have been determined as: m = 2 and b = 4 give the equation of the regression
line.
̂ =𝟐𝒙+𝟒
𝒚
b) Give a predicted weight of a glub of its length is 3.
̂ = 𝟐(𝟑) + 𝟒 = 𝟏𝟎
𝒚