Statistics Spring Semester Exam 2021

You have the following regression equation for the effect of streetlights per block (x), on crimes per month (y): $y=2.4-0.2x$ . How many crimes a month are predicted when there are 7 streetlights on a block?

• 3.8

• 1.7

• 16.6

• 1.0

You have the following regression equation for the effect of streetlights per block (x), on crimes per month (y): $y=2.4-0.2x$ . Calculate the residual for a block with 10 streetlights and 1 crime a month.

• -0.6

• 0.6

• -0.4

• 0.4

You have the following regression equation for the effect of streetlights per block (x), on crimes per month (y): $y=2.4-0.2x$ . Using the regression equation above, correctly interpret the slope

• The effect of the crime rate on streetlights is given by the coefficient –0.2
  

• For every additional streetlight per block, the crimes per month go up by 2.4.
  

• For every additional streetlight per block, the crimes per month decrease by 0.2.

• For every additional crime per month, the number of streetlights goes down by 0.2 lights.
  

Use the sample data set {(8,4), (4,3), (7,3), and (5,2)}. Calculate the least-squares regression line.

• $y=0.3+1.2x$

• $y=-0.02+0.9x$

• $y=1.5+1.5x$

• $y=1.2+0.3x$

Use the sample data set {(8,4), (4,3), (7,3), and (5,2)}. Calculate the correlation coefficient (r). 

• 0.3

• 0.6708
  

• 1.2

• 0.45

• 0.88

A bivariate scatterplot has an  $r^2$  of 0.85. This means

• 15% of the variation in y is explained by the changes in x
  

• 15% of the variation in x is explained by the changes in y.
  

•  85% of the variation in y is explained by the changes in x. 
  

• 85% of the variation in x is explained by the changes in y. 
  

A residual:

• is the amount of variation explained by the least-squares regression line of y on x.
  

• is how much an observed y-value differs from a predicted y-value.
  

•  predicts how well x explains y.
  

• is the total variation of the data points 
  

When looking at a scatterplot of two variables, the variable along the horizontal axis is typically referred to as the:

• response variable

• residuals

• explanatory variable

• categorical variable

Which of the following is a true statement?

• Tests of significance (hypothesis tests) are designed to measure the strength of evidence against the null hypothesis.

• A well-planned test of significance should result in a statement either that the null hypothesis is true or that it is false.

• The null hypothesis is one-sided and expressed using either < or > if there is interest in deviations in only one direction.

A confidence interval estimate is determined from the summer earnings of an SRS of n students. All other things being equal, which of the following will result in a smaller margin of error?

• A greater confidence level

• A larger sample standard deviation

• A larger sample size

• Introducing bias into sampling