A marketing professor at Givens College is int course last quarter follow.

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A marketing professor at Givens College is interested in the relationship between hours spent studying and total points earned in a course. Data collected on 10 students who took the
course last quarter follow.
Hours
Total
Spent Studying
Points Earned
45
40
30
35
90
75
60
65
105
90
65
50
90
90
80
80
55
45
75
65
(a) Develop an estimated regression equation showing how total points earned can be predicted from hours spent studying. (Round your numerical values to two decimal places.)
Transcribed Image Text:A marketing professor at Givens College is interested in the relationship between hours spent studying and total points earned in a course. Data collected on 10 students who took the course last quarter follow. Hours Total Spent Studying Points Earned 45 40 30 35 90 75 60 65 105 90 65 50 90 90 80 80 55 45 75 65 (a) Develop an estimated regression equation showing how total points earned can be predicted from hours spent studying. (Round your numerical values to two decimal places.)
(b) Test the significance of the model with a = 0.05. (Use the Ftest.)
State the null and alternative hypotheses.
O Ho: P1= 0
H B, +o
O Hg: B1 0
B, z o
1.
O Ho: Po+0
H Po= 0
७ H,: B, + 0
H B1-0
O Ho: Bo = 0
H Bo# 0
%3D
Find the value of the test statistic. (Round your answer to two decimal places.)
Find the p-value. (Round your answer to three decimal places.)
p-value =
ww.
State your conclusion.
O Do not reject H,. We conclude that the relationship between hours spent studying and total points earned is significant.
Reject H. We cannot conclude that the relationship between hours spent studying and total points earned is significant.
O Do not reject H,. We cannot conclude that the relationship between hours spent studying and total points earned is significant.
O Reject H, We conclude that the relationship between hours spent studying and total points earned is significant.
:(c) Predict the total points earned by Mark Sweeney. He spent 85 hours studying. (Round your answer to two decimal places.)
points
(d) Develop a 95% prediction interval for the total points earned by Mark Sweeney. (Round your answers to two decimal places.)
points to
points
Transcribed Image Text:(b) Test the significance of the model with a = 0.05. (Use the Ftest.) State the null and alternative hypotheses. O Ho: P1= 0 H B, +o O Hg: B1 0 B, z o 1. O Ho: Po+0 H Po= 0 ७ H,: B, + 0 H B1-0 O Ho: Bo = 0 H Bo# 0 %3D Find the value of the test statistic. (Round your answer to two decimal places.) Find the p-value. (Round your answer to three decimal places.) p-value = ww. State your conclusion. O Do not reject H,. We conclude that the relationship between hours spent studying and total points earned is significant. Reject H. We cannot conclude that the relationship between hours spent studying and total points earned is significant. O Do not reject H,. We cannot conclude that the relationship between hours spent studying and total points earned is significant. O Reject H, We conclude that the relationship between hours spent studying and total points earned is significant. :(c) Predict the total points earned by Mark Sweeney. He spent 85 hours studying. (Round your answer to two decimal places.) points (d) Develop a 95% prediction interval for the total points earned by Mark Sweeney. (Round your answers to two decimal places.) points to points
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Step 2

(a). Develop an estimated regression equation showing how total points earned can be predicted from hours spend studying:

Simple linear regression model:

A simple linear regression model is given as y^ = b0 + bx + e  where y^ is the predicted value of response variable, and x be the predictor variable. The quantity b is the estimated slope corresponding to x and b0 is the estimated intercept of the line, from the sample data.

Given data represents the values of the variables x = Hours spent studying and y = Total points earned for a sample of 10 students.

EXCEL software can be used to obtain the simple regression equation.

Software Procedure:

Step-by-step software procedure to perform a simple linear regression model using EXCEL software is as follows:

  • Open an EXCEL file.
  • Enter the data of Total points earned in columns A and name it as Total points earned.
  • Enter the data of Hours spent studying in column B and name them as Hours spent studying.
  • Go to Data > Data Analysis > Regression.
  • Enter Input Y Range as $A$1:$A$11, enter Input X Range as $B$1:$B$11.
  • Select Labels, Confidence Level and enter the confidence level as 95%.
  • Click OK.

The output is:

Statistics homework question answer, step 2, image 1

From the obtained regression output, the estimated slope corresponding to the predictor variable “X = Hours spent studying” is b = 0.83 and the estimated intercept of the line is b0 = 5.85.

The estimated regression equation showing how total points earned can be predicted from hours spend studying is Total points earned = 5.85 + 0.83*Hours spent studying.

Thus, the regression equation is Y^ = 5.85 + 0.83*X.

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